Teaching Portfolio
Luis A. San Andrés, Professor
Mechanical Engineering Department, Texas A&M University (TAMU)
February 2005

Table of Contents (click below for desired topic)

Personal teaching philosophy

Teaching strategies in the classroom

Educational software and laboratory development

Teaching improvement and assessment

Undergraduate and minority students involvement in research

Personal philosophy about graduate student education

Educational activities with Latin American universities

Future goals as an educator

Appendix A. Syllabus for Mechanical Systems I class

Appendix B. Performance Objectives for Mechanical Systems I class

Appendix C. Syllabus for Mechanical Systems I Laboratory

Appendix D. Pictures of In-class demonstration kits

Appendix E. Ratings from student evaluation forms

My primary area of teaching responsibility at TAMU is the junior level Dynamics and Vibrations course (MEEN 363). I also teach the graduate classes in Mechanical Vibrations (MEEN 617) and Lubrication Theory (MEEN 626).

Personal teaching philosophy (Top)
I believe that students learn only to the extent in which they are motivated to learn. I encourage students to apply their full intellectual potential in the learning process. My teaching philosophy and performance are evidenced by,

  1. the methods I employ to teach the students how to learn the subject matter and not just delivering the class material,
  2. the relevance of the subject material with actual applications that enhance the students experience and formalize their education as responsible engineers,
  3. the learning and practice of effective teaching techniques and modern technology in the classroom,
  4. the permanent development and updating of classes, syllabi and laboratory practices, and
  5. the mentoring and advising of undergraduate and graduate students in the development of their engineering research projects.

In the classroom and in conversations with students I "preach" engineering as a way of life permeated by knowledge and responsibility. I do not spoon feed knowledge nor I prescribe recipes for quick fixes nor I provide plug and chug formulae to satisfy an immediate need. I teach the students how to learn the subject matter, I just not deliver the class material. I follow the Socratic method, always questioning the perceived evidence in search for the truth. I will rarely provide factual answers but most often guide the students to rationalize their experiences of the natural world.

My teaching goal is to prepare students to become real engineers, self-motivated and independent individuals with a wealth of abilities to provide leadership in the technical world. In class I stress the need for keen observation of nature and its behavior, searching for the root cause of measured or observed effects. Once the student "sees" the problem by virtue of applying the fundamental physical laws, we devise the mathematical model governing the dynamics of the system or its components. The most important part of the analysis process is related to the early recognition of the limits and applicability of the model to the actual thing (a system, a hardware component, etc). Next, the solution of the governing equations provides the time evolution or dynamic response (behavior) of the system. The important questions are not just related to the accuracy of the numerical predictions but whether the analysis provides answers to:

  1. How does the system respond with time for any particular type of disturbance?
  2. How long it will take for the dynamic action to dissipate if the disturbance is briefly applied and then removed?
  1. Whether the system is stable or if its oscillations will increase in magnitude with time even after the disturbance has been removed.
  2. What design modifications can be made to the system to improve its dynamic characteristics with regard to some specific application?

An adequate answer to the questions above allows the student to provide firm rationale and sound recommendations that will allow a component or system to be well designed and fulfilling adequately its performance or specified use.

My classes are well organized. I update the syllabus often both in content and form. I try to include the latest advancements in presentation technology and demonstrative software. Fellow teachers comment that I am too organized! An organized class allows me not only to deliver the expected material but also to teach the students how to learn the subject matter while increasing the student experience and confidence. My class syllabi do not merely list grade distributions and schedule of exams. The syllabi describe in detail the expected learning objectives and include weekly descriptions of the material to be taught, reading assignments, homework and laboratory reports. I also provide the students with conscientious policies regarding office hours, scholastic dishonesty and plagiarism. Appendix A lists an example syllabus for the Mechanical Systems I class.

I also developed a comprehensive set of Performance Objectives (PO) for my classes. These instructional objectives, crucial to the teaching and learning process, reveal the student what I intend to teach and what the student should be able to do once he/she completes the course. The POs detail

  1. the fundamental learning goals,
  2. the skills gained in the class which will enhance the student experience,
  3. the required pre-requisite material needed for successful engagement in the class,
  4. the level of student mastery expected for each topic covered in the class.

The POs allow the students to quantify their competence (progress) in the learned material and to qualify their experience in terms of the fundamental concepts grasped, the relevant examples studied and applications envisioned. That is, the instructional objectives provide both depth and breadth on the studied subject. The POs emphasize fundamental concepts leading towards the abstraction of natural phenomena, the modeling and analysis of systems, the mathematical solution of governing equations, and the interpretation of results which stresses sound engineering judgment (and common sense). Appendix B lists the Performance Objectives for the undergraduate class in Mechanical Systems I.

Teaching strategies in the classroom (Top)
I conduct class with a personable approach always accompanied by a nosy curiosity. An adequate interaction with the students is important to create an environment conducive to fruitful teaching and learning. I often incorporate anecdotes and facts from my industrial and research experience. It is not unusual to find me jumping and dancing in the classroom while explaining the students how mechanical systems behave in real life. My humor is sometimes celebrated and other times detested. Nevertheless, I apply myself to keep the students' attention at all times.

The students have access to class notes which I update every semester. These notes include the material taught (overheads), worked examples, useful articles found in technical magazines and journals, and pedagogical material on how to write technical reports or prepare for exams, etc. The class notes and technical report for the Dynamics and Vibrations class are available at webCT.  Class notes for the Lubrication Theory graduate class are available at http://phn.tamu.edu/me626

I initiate every class with an overhead describing

  1. class number and date, reading assignment for next class,
  2. material taught in current class with highlights on the learned concepts,
  3. homework assignment due at an specified later time,
  4. announcements such as a date for an exam or quiz or Career Center Fair, and greetings for a holiday if one is approaching,

I often remind the students about an apparent contradiction: mathematical models are often limited to grasp real world phenomena and yet most often simple models describe with detail our physical world. Whether the model is too complex or too simple is not important as long as it includes the phenomena of interest. That is, only the sound application (and comprehension) of the fundamental physical principles leads to reliable models. Models (and analysis) must be complex by containing all parameters of interest yet still simple to allow accurate predictions in a reasonable time.

I use profusely overheads in my lectures. These are color documents that highlight the concepts of importance. I also use "unfinished" overheads when working examples and problems. As I explain and work the problem I fill the overhead with details of the model, assumptions and calculations. The students follow the same instructions in their class notes. I believe the students retain more knowledge if they are able to see in full color the material learned. Students merely listening to an impersonal lecture or attempting to copy all the scribbles drawn on a board can not be considered as activities engaging the students' participation in the learning process.

The students' learning is enhanced when they actually see the hardware in operation and my desire is to demonstrate the students how well analysis applies to "real life" experiences and daily events. In this regard, I have developed a set of simple yet comprehensive class demonstration gadgets that keep the students focused in the learning process and excited about becoming engineers in a world permeated by technology. Most often I come to class armed with a long slender wood stick or a heavy weight attached to a bungie cord. These two simple gadgets allow me to demonstrate a formidable variety of dynamic system behaviors including excitation of natural frequencies and mode shapes, free and forced responses, and even system instabilities.

At the end of every class period I ask the students to fill a One Minute Paper form which contains the following questions:

    1. What is the most important thing that I learned in class today?
    2. What is the thing(s) that remain unanswered in my mind today?

The One Minute Paper allows prompt student feedback and also serves to gauge the students' understanding of the material taught. Each class period after my introductory overhead I dedicate five minutes to answer all the relevant questions posed in the feedback forms. I have been using the One Minute Paper since 1995 and I consider it as an excellent teaching resource. Its effectiveness, however, seems to decrease as the semester progresses because by then the students are well aware of the class content, organization and expectations. In other words, most students have been able to adapt to my teaching style. In the last weeks of the semester I change the One Minute Paper so that the students address the following questions,

  1. Can you think of an example or actual situation where today's material can be applied?
  2. In simple words, how would you explain to a friend the concept (…) learned in class today?

This variation keeps the students motivated and willing to assess their understanding of the desired performance objectives.

I have students work in groups for homework, take-home exams and quizzes, laboratory tasks and report preparation. I believe that cooperative (team) work is important since it reproduces to a high degree the prevailing working conditions in real life. I challenge the students to become better than the "perfect" student who not only provides detailed work useful just for the current class but that could be considered as a reference or resource in his/her future professional work. A grade of 10 implies the perfect work. However, I do not limit grades to this top qualification. I have been pleasantly surprised through the years at how students working in groups excel in their work. By the end of the semester, groups of students compete fiercely because they have far exceeded the expectations of an elusive perfect student. The students are able to recognize the fruits of relevant work and feel good about their performance. Homework final grades have been at times 50% higher than the maximum value allotted at the start of the class.

I regularly conduct midterm class evaluations. The students provide answers to the following form:

Since we are in this together, list at least as many items in answer to question (1) as you do for question (2).

  1. What can you do to help you learn more?
  2. What can I do to help you learn more?
  3. What, if anything, am I doing that you want to be sure I continue doing? The answer to this question is important since I will have to make choices based on the answers to the above questions and don't want to stop doing what you find most effective.

The students’ feedback allows to strengthen the teaching goals and aids to modify the teaching strategy (if needed) to either allocate more time for worked examples or to review in depth some fundamental material. I realize that I must adapt my teaching so that I can provide meaningful instruction to students who have a myriad of learning styles. In all cases I try to be proactive and attentive to the students’ requests. I also try to facilitate learning and (in my point of view) grades are ultimately not important. I am a dedicated and conscientious teacher and I want all students to try learning as hard as I also try to impart knowledge. An efficient teaching method does not need to relax the requirements for technical competence in the material learned.

I prepare exams fully aware of the inherent time limit and taking into consideration their stressful nature and impact in the tight schedule of the students. The exams contain multiple problems that address to a specific skill or knowledge to be mastered by the students. I pay particular attention to the wording in each question and detail the partial grade distribution for each problem. The exams include a number of short answer questions, true or false, that evaluate the student's grasp of fundamental concepts. I stress not only the procedure to solve the engineering problem but more importantly the relevant physical magnitude of the answer. There is little knowledge gained with the "right answer" when this is not accompanied by the sound judgment of its physical magnitude and its relevance to the life and/or performance of the mechanical component or system studied. In all exams I request the students to certify a non-cheating individual work policy as per the TAMU Aggie Code of Honor.


Educational software and laboratory development (Top)
In 1994, Professor John Vance and I revamped the content of the undergraduate Mechanical Systems I Laboratory to include practical experiences providing the students hands-on-experience for the experimental identification of system physical parameters and the measurement of the time response of dynamic systems. Both instructors have made a conscientious effort to help the students in the preparation of self-contained and accurate technical reports. The instructional material also includes the evaluation of uncertainty in experimental single sample measurements. This topic is of fundamental importance to render reliable measurements of practical use and which provides the student with a clear understanding of the limitations of experimental techniques, accuracy of sensors, instruments and A/D data conversion. I have also developed a format for report presentation that follows the technical memorandum used frequently in industry. Appendix C details the laboratory syllabus, policies, report format as a technical memorandum and an introduction to uncertainty in experimentation. (Note: This class was phased out in 2000, when the new curriculum in MEEN was set in place)

In general it is believed that graduate classes are mainly theoretical with emphasis on advanced mathematical analysis. However, simple demonstrative experiments are worth a thousand times more than complicated verbal descriptions of physical behavior. To this end I have developed with the help of graduate students several experimental rigs and kits for demonstration in the Mechanical Systems I (MEEN 334), Lubrication Theory (MEEN 626) and Mechanical Vibrations (MEEN 617) classes. The demo-kits include simple mass-spring-damper systems (1- and 2-DOF), a miniature power plant and rotor kits demonstrating fluid film bearing whirl and whip instabilities, squeeze film damper behavior, etc. Appendix D shows photographs of some of the demonstration rigs I have developed or purchased and modified. My Principal Investigator research incentive return funds have been used for the construction or acquisition of the demonstration rigs.

I also present in class systems’ simulations using a personal computer. The students are taught how a particular system responds to dynamic inputs (theory and solution of ODEs). Next, the MATHCAD© software I have developed allows the students to observe in real time the system response due to changes in the input parameters. Several worksheets demonstrating the dynamic response (vibrations) of single and multiple degree of freedom systems can be downloaded from the URL site http://phn.tamu.edu/me617


Teaching improvement and assessment (Top)
I am familiar with the principles of active teaching and collaborative learning. I have attended a number of teaching workshops and seminars on the subject and implemented some of the cooperative teaching techniques on my classes. My student teaching evaluations show continuous improvements. Although these are important, I do not consider the evaluations as the sole source to base my teaching performance. Undergraduate students regard me as a tough instructor who pushes them to work too hard. My notorious reputation is perhaps a reflection of my dedication to impart meaningful knowledge.

Appendix E provides the statistical data available from the Student Evaluation Forms. The students reply to the following ten questions. A score of five (5) gives the highest rating while one (1) indicates the lowest:

  1. Lecture preparation: lectures are consistently well prepared and organized
  2. Assignments: course requirements, assignments, projects, etc, aid course objectives and are fair and evenly distributed.
  3. Communication: the instructor clearly explains material to a group.
  4. Responsiveness: the instructor is open to students’ questions and effectively answers them.
  5. Academic concern: the instructor seems to care whether the students learned.
  6. Availability: the instructor willingly makes time to help students.
  7. The instructor is fair and consistent in evaluating student performance.
  8. Environment: the instructor maintained a good learning environment in the lass.
  9. All things considered, this was a good course.
  10. All things considered: the instructor was an effective teacher.

In addition to these ten questions, the students also provide valuable written comments and feedback related to the following questions:

  1. What are the most positive aspects of this course.
  2. Grading has been fair and consistent. Indicate Yes or No. If No, tell why.
  3. What qualities did you like most about your instructor?
  4. What qualities did you like least about your instructor?
  5. Additional comments about the course and instructor.

The students' written comments for the classes I have taught are available upon request. A few of the students’ comments, quoted verbatim from the evaluation forms, follow:

MEEN 334, Mechanical Systems I

"Was an excellent class that brought the aspects of many parts of the engineering concepts that we had previously learned together and linked them in several ways." – Spring 1991.

"Instructor wants students to understand material fully. Not just use formulas to find a solution," – Spring 1992.

"He was very eager to work with us and always emphasized that we come to him if we were having problems with something. Even though he had much to do outside class with his research work, he still had time for us." – Spring 1991.

"Did listen to criticism and changed lecture style – helped," – Spring 1992.

"In class he was concerned whether students understood the material. The one minute papers helped him to know where problems area where." – Fall 1994.

"One of my first professors who id not see gender as an issue, very good." – Fall 1994.

"He put a lot of effort in the class. He was always available out of class time and always had extra-credit opportunities. Tried to relate real-life situations to material," – Spring 1994.

"He is a damn good teacher and he knows his material very well. He is easy to learn from and he gets the material across very well. I hope to have more professors like in my future classes." – Fall 1996.

"Very passionate about engineering: admits mistakes." – Fall 1997.

"Actually asks for feedback (one minute paper) and tries to adjust accordingly. Keeps his door open. Has a wonderful policy "No grade is final." This instills optimism instead of pessimism. Gives bonus for extra effort. He recognizes the massive amount of time spent in course." – Fall 1998.

MEEN 617, Mechanical Vibrations

"Notes and overhead helped a great deal in understanding the class, also demonstrations were interesting." – Fall 1993.

"This is your best class and the best class I have taken at A&M. Keep the good work." - Spring 1996.

"Very organized and well prepared lectures. Willing to answer questions. Makes time to answer questions. Concerned about what was learned not just what was done." – Spring 1997.

MEEN 626, Lubrication Theory

"He has a very deep and vast knowledge of the class material and thus, was able to effectively communicate the most important aspects." – Spring 1993.

"The instructor allows the chance to review and modify the material of the homeworks to improve the grade." – Fall 1995.

"He gives very goo explanations and makes clear concepts which were not as clearly explained with other instructors. Best class I ever had at A&M’" – Fall 1995.

"Caring that we understand and learn. Focus on quality of education. Attention to detail. His wealth of knowledge and understanding pertaining to this subject." – Fall 1997.

The summary of scores from the students' evaluations and the students' written comments demonstrate that I am a very effective teacher in the graduate level classes. In 1998 I received a departmental Outstanding Graduate Teaching Award and based on favorable comments and recommendations from the graduate students in my classes. I have improved notably my communication skills with the undergraduate students and I am more sympathetic to their busy schedules. I am also aware that I need to shape a teaching style which accommodates a wide and dissimilar audience, ranging from students with great interest in the topics studied to others with just marginal or passing interest in engineering.

At times I have noted that some of my undergraduate students expect to be evaluated solely on the basis of their attempts to try and not on their competence in the studied field. This condition has become pervasive in education as documented by the many editorials published in major education and newsmagazines. I remain firm in my belief that students earn their grades and this best serves the university’s goal to produce technically competent engineers.

Undergraduate and minority students involvement in research (Top)
I recognize the need to identify early on talented undergraduate students and to offer them an opportunity to perform guided research. I have acted since 1992 as an advisor to the TEES Undergraduate Summer Research Program and provided a research environment to several undergraduate students (including 5 females, 7 Hispanics, 2 Afro-American). I also volunteer to display my research and teaching advances to high school students at the TAMU Science, Technology & Youth Symposium held yearly in March.

I have published well over 100 journal papers, 80+ co-authored with graduate students, many of them minority.

Distinctions – Former Students (Female and Hispanic)

Name

Society

Distinction

Contribution

Deborah Osborne- Wilde

ASME Tribology Division

2004 Marshal Peterson Young Investigator Award

Gas Bearings and Seals

Sergio Diaz

ASME Tribology Division

2003 Burt Newkirk Investigator Award 

Squeeze Film Dampers

Nicole Zirkelback

Texas A&M University

1998 Outstanding Graduate Student Award

Gas Annular and Face Seals

  Several graduate and undergraduate students have obtained STLE scholarships and fellowships

 

2004 BEST Rotordynamics Paper Award IGTI  Structures and Dynamics Committee)

Rubio, D., and L., San Andrés, 2004, “Bump-Type Foil Bearing Structural Stiffness: Experiments and Predictions”, ASME Paper GT 2005-53611 (accepted for publication at ASME Journal of Gas Turbines and Power)

2003 Best Rotordynamics Paper Award (IGTI, Structures & Dynamics Committee)

Wilde, D.A., and San Andrés, L., 2003, “Experimental Response of Simple Gas Hybrid Bearings for Oil-Free Turbomachinery,” ASME Paper GT 2003-38833, ASME Turbo-Expo 2003 Conference, Atlanta, GA, June (accepted for publication at ASME Journal of Gas Turbines and Power).

 


Personal philosophy about graduate student education (Top)
I believe that work leading towards an advanced graduate degree should give the students a thorough and comprehensive knowledge of their professional field and training in methods of research. The final basis for granting the degree shall be the candidate’s grasp of the subject matter of a broad field of study and a demonstrated ability to do independent research. In addition, the student must have acquired the ability to express thoughts clearly and forcefully in both oral and written languages. The degree is not granted solely for the completion of course work, residence and technical requirements, although these must be met.

It is my belief that an advanced graduate degree is not granted because:

  • the student has merely written a few thousand lines of a computer code and verified its execution for several instances of some physical parameters without regard for the certainty of the predicted values or due consideration for the usefulness of the code to other members of our profession, or
  • the student has performed some experiments and measurements in an existing test facility without a thorough understanding of the physical principles involved in the operation and performance of the studied mechanical device.

I believe that my role as a graduate student advisor to the potential MS or Ph.D. candidate includes:

  • Provision of the means to conduct the research work (i.e. financial support, adequate office space in an environment conducive to scholarly activities, computational facilities, adequate software, and access/acquisition of papers, textbooks, etc.).
  • Guidance on the relevant literature related to the studied subject with suggestions for further reading and understanding on the major research topic.
  • Guidance on the proper use and selection of measurement techniques, instruments and sensors, and overall design of experiments.
  • Guidance on the proper selection of sound and efficient mathematical analysis and computational algorithms for the solution of the research problem of interest.
  • Conduct regularly scheduled meetings with the student to discuss progress and shortcomings, advantages/ disadvantages of a selected model or technique, major assumptions and limitations of the analysis (theoretical and computational), workarounds to overcome major modeling difficulties, suggestions to minimize computer execution time, strategies for efficient programming and/or testing, etc.
  • Edit technical manuscripts (written contributions) from candidate as per their scientific content and compliance with the guidelines of archival journal publications.
  • Recommend classes, seminars, etc. for the student to attend or audit, and such that these not only enhance the student’s depth in the researched field but also provide breadth and competence in the professional field.
  • Serve as an active co-author with the student for joint scholarly (per reviewed) journal publications by providing ideas and concepts, discussion of results, etc.

On the other hand, I believe my role as an advisor does not include the following activities,

  • Conduct minute scrutiny of the student progress.
  • Monitor correctness of analysis, equations, computer programs, etc. in every single detail.
  • Edit as per correct use of English and literary style each document, technical report and manuscript prepared by the student to show his/her research progress.
  • Teach the basic mathematical and engineering skills the student should have learned in his/her prior education.

I expect from a graduate student performing research under my direction:

  • To complete his/her work (assigned tasks and responsibilities) to the best of his/her ability.
  • To take full responsibility for his/her accomplishments and shortcomings.
  • To have a strong desire to learn and be of assistance to his/her fellow students in the Laboratory


Educational Activities with Latin American Universities (Top)
I also pursue active collaboration with universities and research centers in Mexico, Venezuela, Brazil and Ecuador. I have developed strong educational and research ties with IIE, CENIDET and CIATEQ in Mexico, Universidad Simón Bolívar in Venezuela and Escuela Politécnica in Ecuador. My desire is to disseminate the strong educational curriculum program at TAMU and the technical expertise of the Turbomachinery Laboratory to the Latin-American countries. I have also offered assistance in developing modern engineering curriculum in these countries and brought talented engineers to pursue graduate students at TAMU.

Future Goals as an Educator (Top)
My academic career is committed to teach students in Mechanical Engineering and to conduct useful research in the fields of tribology and rotordynamics. I have come a long way since I started teaching at TAMU. In the beginning I had virtually no prior training and expertise to undertake such vital activity conducive to prepare engineers working for the good of society. In many respects I learned the hard way, i.e. I gained knowledge and experience from many mistakes and by pumping timeless energy to reduce my shortcomings. I have become better prepared to teach well students who have dissimilar backgrounds. After all these years I remain excited and curious about the simplest of things and permanently perplexed by the beauty of mathematics and the sheer simplicity of nature's behavior.

On the coming years ahead I pledge to keep my ingenuity. I will remain an attentive listener of the students' concerns and desires. I would like to become more proficient in the use of modern object oriented programs and software. Enhanced computer based skills will allow me to better prepare and to present timely the class material. I also have a very detailed description of my research work and laboratory at the World Wide Web. The design of our web site has been selected by the Mechanical Engineering Department to display the many research areas at TAMU.

I will continue to believe that the education of a young engineer is more valuable than the thrill work in a research project or a cold impersonal journal publication. I will continue to learn more (and apply) modern teaching techniques with a special emphasis on group learning and organized cooperative activities. I also would like to mentor young faculty as they initiate their academic careers and face important challenges and responsibilities.

 

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Appendix A

Syllabus for Mechanical Systems I class
Dr. Luis San Andrés
Instructor Fall 1998
(Top)

Course Description:         Modeling and analysis of dynamic systems using classical techniques. Formulation and solution of systems equations, introduction to instrumentation and data acquisition.

Prerequisites:        CVEN 205, MEEN 213, MATH 308; Corequisite: MEEN 357.

Course Goals: To introduce the fundamental concepts for modeling dynamic systems, particularly discrete parameter mechanical systems, to derive differential equations of motion and determine systems dynamic response, and to provide knowledge for practice in understanding systems behavior.

Lecturer: Dr. Luis San Andrés, ENPH 118, Phone - 845-0160, LsanAndres@Mengr.tamu.edu

Office hours: T: 12:30-1:30p.m., W: 4:00-5:00 p.m., R: 10:00-11:00 a.m., or by appointment.

Class Time: 501/502/503, T,R 8:00-9:15 a.m., ZACH 127B

Labs: 501 - T 2:20-5:10 p.m., 502 - R 2:20-5:10 p.m., R - 11:10-2:00 p.m. ENPH 301.

References: System Dynamics, an Introduction, D. Rowell and D. Wormley, Prentice Hall Pubs, 1997.

MEEN 334 Class Notes (handouts), L. San Andrés, TEES Copy Center, WERC 221.

MEEN Laboratory Manual (URL sites phased out – not public access)

Other:                   Dynamics of Physical Systems, R. H. Cannon, McGraw-Hill Pub. Co, 1967.
Analysis and Design of Dynamic Systems,
Cochin, I., 1997, Addison-Wesley Pubs.
Engineering Mechanics, Vol. II: Dynamics, J.L. Meriam, L. Kraige, J. Wiley Pubs., III, 1992.
Vibrations of Mechanical and Structural Systems, L. James, Harper & Row
Pubs., N.Y., 1989.
Mechanical Vibrations, S.S. Rao, Addison-Wesley Pubs., 2nd Ed., 1990.

EXAM SCHEDULE:   1: Physical & Mathematical Modeling,              Wed., Oct. 7,         7-9:00 p.m. Zach 102
2: Dynamic Response of Systems,                    Wed., Nov. 11,
7-9:00 p.m. Zach 102
3: Final Comprehensive Exam, 501/502/503, Mon., Dec. 14,1:-
3:00 p.m. Zach 127B

Grading: Practice problems assigned but not graded. GRADED group take-home quizzes every Tuesday and turned in on Thursday. Two in-class exams and a comprehensive final exam. Exams will cover the material specified in the Meen 334 PERFORMANCE OBJECTIVES. No make-up exams will be given unless the student has an acceptable and verifiable excuse, and notified the lecture instructor in advance. (If the instructor is not in his office leave a [phone or e-mail] message and return address or phone number).

                   Take Home Quizzes          10%    (assigned Tuesday, turn in Thursday) Group work only.
                   Laboratories                     30%    (see Laboratory Syllabus for grade policies)
                   First Exam                        20%             
                   Second Exam                    20%
                   Final Exam                       20%    (Final is NOT optional nor will be waived)
                                                          100%

Your Take home quiz grade can be higher than 10%. In fact many student groups make 13 to 15%. How? By presenting detailed (and neat) quizzes that fully describe the solution of the problem(s), the steps in the modeling and procedure of solution, include a nomenclature and a sound discussion of the results obtained.

Note: All background material on prerequisites is the responsibility of each student (See page 5 of this handout).See a full description of Performance Objectives at class URL site

 

Meen 334, Class Syllabus         Fall 1998, Zach 127B        

Chp: indicates chapters from Rowel and Wormley reference book, HD: Dr. San Andrés class notes

w#

dates

Lecture Material (subject to revision)

Reading Assignment

1

08/31

Course Introduction Importance of system dynamics analysis and design. Review of dry friction and rolling friction. Operating point and example of dynamic response of a mechanical system.

HD#1, Chp. 1, pp. 1-14

HD #2

2

9/07

Physical Modeling of Lumped Parameter Mechanical Systems Equivalent Stiffness (K), Inertia (M) and Damping (D) Elements and associated potential & kinetic energies and power dissipation. (K,D,M) Elements for translational and rotational motions.

HD #2,

Chp. 2, pp. 19-37

3

9/14

Mathematical Modeling of Mechanical Systems Review of dynamics of particles and rigid bodies for motions in a plane. Conservation of linear and angular momentum.

HD #5: Examples,

Chp. 5, pp.120-145,

4

9/21

Equations of motion in mechanical systems Constraints and Degrees of Freedom. Free response (due to initial conditions) of mass-spring oscillator - The concept of harmonic motions and natural frequency . Linearization of non-linear mechanical systems.

HD #5: Examples

Chp. 3, pp. 83-89

5

9/28

Electrical and Fluidic Systems Electrical resistor, capacitance and inductance: constitutive equations. Principles of conservation (Kirchoff’s Laws). Fluidic capacitance and resistances. Thermal capacitance and resistances. Analogies to mechanical systems.

HD #3 & #4

Chp. 2, pp. 37-44, 44-53, 53-59

6

10/05

Review Oct. 7, Wed. 7-9 p.m.

Principle of operation of DC motors

Zach 102, EXAM I

7

10/12

Dynamic Response of First Order Systems. Derivation of equation of motion for first order systems. System Free Response due to initial conditions. The concept of time constant and its effect on the speed of response. Methods to identify (measure) a system time constant. System Dynamic Forced Response to Simple External Functions:Step and Ramp. Response to an Impulse Forcing Function

Chp. 9, pp. 276-294,

HD #6a,b

8

10/19

Dynamic Response of Second Order Systems. Response of Undamped Systems. The concept of natural frequency revisited. Types of response: underdamped, overdamped, critically damped systems.

Chp. 9, pp. 309-320,

HD #7a

9

10/26

Free response due to Initial Conditions. The concept of logarithmic decrement and damping ratio and its effect on the dynamic response. Method to identify damping and natural frequency of a system.

HD #7a,b

10

11/02

Forced Vibrations Response to Simple External Loading Functions: Impulse, Step and Ramp Responses. Steady State values.

HD #7b

11

11/09

Review Nov. 11, Wed. 7-9 p.m.

Review of numerical solution of ODE’s Short review of Eulers’ method and numerical stability (artificial numerical viscosity)

Zach 102, EXAM II

12

11/16

Frequency Response of First Order Systems Dynamic Response to Periodic (Harmonic) Excitations. Interpretation of amplitude and phase angle of dynamic response. Uses of a low pass frequency filter.

HD #6c

Chp. 14, pp.453-472

13

11/23

Frequency Response of Second Order Systems Frequency Response (Amplitude and Phase angle) for constant magnitude force and imbalance forces. Interpretation of regimes of operation.

HD #7d,e

Thanksgiving Nov. 26th

14

11/30

Understanding Frequency Response Functions: Regimes of operation: below, above and around the natural frequency. Force diagrams. Force transmissibility and design considerations for foundation isolation.

HD #7e,f

15

12/07

Examples and Applications: Vibration isolators Tues. 12/08

Last day of class

16

12/14

501-502-503: Mon., Dec. 14, 1:00-3:00 p.m.

ZACH 127B, FINAL EXAM

Important note, Chapter 8.3: Classical solution of linear differential equations is responsibility of student.

Policies Meen 334 - Mechanical Systems I. Fall 1998 - Dr. Luis San Andrés

About Handouts: The handouts used in this course are copyrighted. By "handouts," I mean all materials generated for this class, which include but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and additional problem sets. Because these materials are copyrighted, you do not have the right to distribute freely the handouts, unless the author expressly grants permission.

About plagiarism: As commonly defined, plagiarism consists of passing off as one’s own ideas, words, writings, etc., which belong to another. In accordance with this definition, you are committing plagiarism if you copy the work of another person and turn it in as your own, even if you should have the permission of that person. Plagiarism is one of the worst academic sins, for the plagiarist destroys the trust among colleagues without which knowledge and learning cannot be safely communicated. If you have any questions regarding plagiarism, please consult the latest issue of the Texas A&M University Student Rules, under the section "Scholastic Dishonesty."

Practice problems will be assigned as the semester progresses. These will not be graded, but they are good practice for the exams. It cannot be emphasized enough that the way to learn how to work problems is to work problems. Use the given answer only to determine that your strategy, your procedure, and your numerical computations are correct. Working backwards from the answer will not teach you the engineering method, or the principles involved in the problem.

Solutions to practice problems will not be posted. I suggest students should take advantage of office hours to obtain help in developing clear procedures for solution of problems and to improve their understanding of class materials. The instructor will not solve problems for you on office hours; instead he will help you learn an engineering method for problem solving. The class handouts include many worked examples and solved exam problems that will allow you to study best for this class.

Take-home quizzes will be assigned every Tuesday and must be turned in Thursday. Quizzes will be worked in groups of 3 or 4 students (perhaps the same groups as those assigned in Lab). Quizzes will be graded and returned in class the following week. Please note that quizzes make 10% of your total grade. Solutions to quizzes will be posted at the TEES Copy Center located on the second floor of the WERC building. There will be no excuses for missing quizzes.

Those portions of the textbook devoted to mechanical (structural) systems will be the main subjects of the course, but a few electrical and hydraulic systems will be considered also, and their analogies to mechanical systems will be emphasized as an aid to modeling. The lectures will broaden the coverage of the textbook and provide examples of analysis as applied to the design and troubleshooting of mechanical systems. There will be significant amounts of subject material mentioned in the lectures which are not in the textbook. The textbook is not a complete reference for this course. The class notes of Dr. Luis San Andrés are available at the TEES WERC Copy Center or can be downloaded from URL site. Attendance and attention to the lectures are therefore mandatory for success. References for outside reading will be recommended in class.

About office hours: The purpose of office hours is to encourage individual interaction between the students and the instructor. The nstructors is available to discuss not only questions related to the course, but other issues where I can help as a professional engineer, educator and researcher. Please take advantage of office hours. To utilize this time efficiently, students should prepare by organizing questions in advance.

I am willing to help you at times other than office hours without an appointment. However, just like you, I have responsibilities other than MEEN 334 (teach other classes, direct graduate student research, write proposals and technical papers, organize laboratories, voluntary work for ASME, etc.). I must budget certain times to meet those responsibilities. My weekly work schedule is posted outside my office. Please do not be offended if I am in the office but cannot meet with you. The use of e-mails for communication with your instructor is acceptable. I usually receive three types of e-mail messages:

  1. a request to schedule a meeting at other times than office hours. I will provide you with an exact date and time for the meeting,
  2. questions related to the impending take-home quiz due (say) next day,
  3. questions related to the study material for an exam.

I reply promptly to all messages (usually within the next hour).

I recommend the following relevant problems from the reference book System Dynamics, an Intoduction, by D. Rowell and D. Wormley, Prentice Hall Pubs, 1997. X-copies available at WERC copy center.

Some of these problems may be assigned as weekly quizzes or may appear in any of the exams. Work (with your group) as many problems as possible. After all, the exercises will benefit you and the more you practice the better you will become!

Chapter

Topic

Problem number

1

Introduction

2

2

Energy and Power Flow

1,4,5,6,9,15

3

Primitive one-port elements

1, 9

5

State equation formulation

4,5,8,10,12,16,21

8

Solution of ODEs

12,14,18

9

System response

2,4,6,11,12,13,14,16,23,24

14

Frequency response

5,6,14,17,19,20,23

Prerequisites for Meen 334:

MEEN 213: Engineering Mechanics II

Plane kinematics and kinetics of Rigid Bodies.Free Body Diagrams, Area and Mass Moment of Inertia.

Newton’s Laws of Motion: Conservation of Linear and Angular Momentum.

Principles of Work and Energy, Impulse and Momentum.

Correct use of SI and U.S. Customary units. Conversion skills and equivalence of units.

MATH 308: Differential Equations:

Solution of Linear Ordinary Differential Equations by Laplace transforms including inverse transformations and partial fraction decomposition.

Systems of differential equations. Basic Theory of complex numbers and conversion from cartesian to polar representations.

CVEN 205: Engineering Mechanics of Materials

Concepts of Stress and Strain. Material Properties. Deformation and Forces for axially loaded members.

Torsion and Flexural (bending) deformation in structural members.

Combined Loading. Axial Deformation (buckling) of long beams.

OTHER things you should know:

  • Vector Algebra and Calculus.
  • Matrix Algebra including evaluation of determinants and solution of systems of linear algebraic equations.
  • Basic knowledge of computing languages on operating system of your choice.
  • Knowledge of simple electrical circuits and Kirchoff’s laws. Ability to formulate the voltage vs. Current relation to resistors, capacitances and inductances.

AND LAST BUT NOT LEAST: DESIRE AND WILL TO LEARN !!

See a full description of Performance Objectives at class URL site

 

GLOBAL PERFORMANCE OBJECTIVES

  1. Physical Modeling of Mechanical Systems: You should be able to identify the fundamental components of mechanical systems into generalized lumped mass (inertia) M, stiffness K, damping D elements. Determine the degrees of freedom and/or the constraints present on the system. Establish the equivalence of Kinetic and Potential (Strain) Energies in Conservative systems.
  2. Mathematical Modeling of Mechanical Systems: You should be able to derive the fundamental equations governing the motion of lumped-parameter mechanical systems in general plane motion. Fundamental knowledge of the kinematics and kinetics of planar rigid body motion: rectilinear motion and rotational motion about a rigid axis. Concepts of relative velocity and acceleration should be mastered.
  1. Determine the Dynamic response (Solution) of first order systems as described by the ODE: for initial conditions; and define the Time constant of system. t = M/D and its effect on the system speed of response. Determine the Characteristic Response to Impulse, Step and Ramp External Forcing Functions as well as the Frequency Response for Periodic Excitations. Identify the Applications of first order systems.
  2. Determine the Dynamic response (Solutions) of second order (oscillatory) mechanical systems as described by the ODE: for initial conditions. Discuss the concept of natural w n frequency of a system. Establish the Characteristic Response to Initial Conditions for damped systems. Derive the dynamic response to Impulse, Step and Ramp External Forcing functions, and discuss the concepts of transient and steady state responses. Discuss the concept of damping ratio and the effect of damping D on the amplitude and speed of response of a system. Derive the dynamic response to periodic (harmonic) external forcing functions and establish the regime of operation of a system below, close to, or above its natural frequency. Discuss the Amplitude of motion and Phase lag of response based on the system. Discuss the concept of Frequency Response Function (FRF). Identify the applications of second order systems.
  3. Be able to handle correctly physical units in both SI and English systems. Be able to estimate order of magnitude of answers to the many physical problems found in the class homework, exercises and exams.

VERY, VERY IMPORTANT NOTE: Mathematical procedures and analysis in assignments and exams will be regarded as erroneous if physical units are handled incorrectly. The least we can expect from conscientious students (potential mechanical engineers) is the correct usage and conversion of physical units and the ability to estimate the right order of magnitude of an answer to an engineering problem.

In my experience, common sense is a must for a successful engineering career!

Meen 334 - Index to Class Notes

Dr. Luis San Andrés - Total number of pages = 179

TEES Copy Center, WERC 221 and class URL site

0. Cover and Index ( 2 pages).

  1. Introduction to mechanical systems. (9 pages)

Definition, Classifications, Definition of Analysis, Synthesis and Design, Steps in Modeling, Definitions of Free and Forced Responses, First and Second Order Systems, Differential Equations: Classification and Nomenclature.

            Appendix A. Dry and rolling friction (12 pages)

  1. Modeling of Mechanical (Lumped Parameter) Elements. (14 pages)

Fundamental elements in mechanical systems: inertias, stiffness and damping elements. Review of dry and rolling friction models. Equivalent spring coefficients and associated potential energy. Equivalent mass or inertia coefficients and associated kinetic energy. Equations of motion of a rigid body in a plane. Equivalent damping coefficients and associated dissipation energy. Types of damping models (linear or viscous and nonlinear). Elements in series and parallel.

3. Modeling of Lumped Electrical Elements. (7 pages)

Fundamental elements in electrical systems: resistances, inductances and capacitors. Review of fundamental Ohm’s Law and Kirchoff’s Law. Equivalent electrical resistances and associated dissipation energy. Equivalent capacitors and associated electrostatic energy. Equivalent electrical inductances and associated electro-magnetic energy. Elements in series and parallel.

4. Modeling of Thermal and Fluidic Elements (12 pages)

a) Modeling of Thermal Elements

Fundamental elements in thermal systems: capacitances and conductances. Elements in series and parallel.

b) Modeling of Fluidic Elements.

Fundamental elements in fluid transport systems: damping or drag coefficients, fluidic resistances, capacitances and inertances. Types of flow: laminar and turbulent. Elements in series and parallel.

  1. Examples: Derivation of Equations of Motion and Initial Conditions in Simple Mechanical Systems. Linearization. (34 pages) X-copies only.
  2. Dynamic response of first order mechanical systems. (26 pages).

          a) Free response to initial conditions: Systems with dry-friction and viscous damping.

            b) Forced response: step, ramp and periodic loads.

            c) Frequency response function of first order systems: response to periodic loading.

  1. Dynamic response of second order mechanical systems. (59 pages)

          a) Free response to initial conditions.

            b) Forced response: impulse and step loads.

            c) Frequency response function of second order systems: response to periodic loading

            d) Interpretation of forced periodic response.

            e) Transmissibility (forces transmitted to base or foundation).

          f) Frequency Response due to Base or Foundation Motions.

Additional material: Old exams and worked problems (54 pages) X-copies only.

 

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Appendix B

Performance Objectives for Mechanical Systems I class
Dr. Luis San Andrés
Instructor Fall 2000
(Top)

                                   

I. GOALS

The general goals of Mechanical Systems I are for you (the student) to learn methods of modeling, analysis, and design of physical systems under dynamic conditions of operation. Mechanical Systems I covers the dynamic (time) response of simple (1 degree of freedom) structural mechanical systems, basic electrical circuits and DC motors. An introduction to the analysis of more complex (multiple degree of freedom) systems is also provided.

II. PREREQUISITES

A. Dynamics - knowledge of particle and planar rigid body kinematics and kinetics. Knowledge of work - energy relationships.

1. Student must be able to draw free body diagram of particles and rigid bodies including all external forces and moments acting on a body. You must be familiar with the appropriate physical units for forces and moments in both SI and U.S. customary units.

2. Student must be able to relate positions, velocities and accelerations, as well as angular positions, velocities and accelerations for any moving set of particles or two points on a rigid body in different coordinate systems.

3.         Student must be able to calculate the mass of rigid bodies given a mass distribution and geometric information. You must be able to calculate and look up (in books) the mass moments of inertia for a rigid body about any coordinate axis. Use the parallel axis theorem to calculate mass moments of inertia about axes parallel to a given axis where the moment of inertia is known. Find area moments of inertia, distinguish them from mass moments of inertia, and know where they are useful in structural mechanics.

4.         Given a complete free body diagram of a particle or rigid body, you must be able to write a vector differential equation for the translational motion of a particle or the center of mass of a rigid body by summing forces in appropriate directions. You must recognize these as differential equations valid for all times starting from some initial system configuration and not merely as algebraic equations. You must be able to sum moments on rigid bodies and write differential equations for rotational motion. You must be able to sum moments about the mass center, a fixed point, or an arbitrary point on the rigid body.

5.         Student must be able to define the concepts, and derive expressions for the kinetic and potential energies of a rigid body. Explain the equivalence of kinetic and potential energy in conservative systems.

6.         Given a designated power source (horsepower or watts), student must be able to calculate the energy transfer to a flywheel or elastic storage medium over a given time, with or without energy dissipation (losses).

7.         Given the torque and rotational speed of a prime mover, student must be able to calculate the available power (horsepower or watts).

B. Strength of Materials - Student must be able to define the fundamental constitutive relationship for the motion and deformation of linearly elastic materials (Hooke's Law). You must be able to derive the appropriate differential equations for the elastic deformation of axially loaded bars, beams under bending, and torsion of rods. Student must be able to calculate deflections, strains and stresses in simple elastic members under a variety of point and distributed loads. You must be able to determine the strain energy of simple elastic elements like axially loaded bars and beams under bending.

C. Mathematics - Student must be able to perform basic calculus, vector and matrix operations.

1.         Student must be able to solve systems of linear equations using Cramer's rule or numerical analysis techniques. (Up to 3x3 by hand and larger systems with calculator or computer).

2.         Student must be able to differentiate trigonometric, polynomial, and exponential functions. You must be able to use the chain rule for differentiation.

3.         Student must be able to solve first and second order ordinary differential equations with constant coefficients by Laplace methods or differential operators techniques. Student must be able to distinguish homogeneous and non-homogeneous ordinary differential equations, and identify the fundamental and particular solutions to the equation.

4.         Student must be able to add, subtract, multiply, and divide complex numbers in both polar and cartesian form; and, convert between cartesian and polar representations using Euler's identity.

5.         Student must be able to handle basic trigonometric operations involving sines, cosines and tangent functions and their respective inverse functions. Student must be able to compute the inverse tangent of a ratio of numbers defining the sides of a triangle and be competent in identifying the correct

quadrant for the angle obtained.

6.         Student must be able to distinguish between linear and non-linear differential equations. You must be able to prove the principle of superposition for linear systems of equations or ordinary differential equations.

D. Electricity - Student must be able to master basic electricity and magnetic principles from physics. You must be able to formulate the general relationship between voltage and current in a resistor, determine the power dissipated in a resistor, and physically explain the conversion of energy in a resistor. Student must have some basic knowledge about the physical principles of operation of capacitors and inductances.

 

III. PERFORMANCE OBJECTIVES

A.        Student should be able to develop mathematical models describing real mechanical systems. Make appropriate assumptions to identify the relevant system parameters affecting the operation (dynamic response) of a real system. You should be able to characterize the system structure in terms of lumped inertia, stiffness and damping elements performing unique energetic functions. Student must be able to derive sets of coupled ordinary differential equations and algebraic constraint equations representing the state of motion of systems which encompass a single domain or multiple domains, i.e. mechanical and electrical, for example.

1.        Student should be able to model the behavior of a mechanical translational and rotational inertia (mass or moment of inertia) by relating the velocity or angular velocity of the element to the momentum of the inertia. Calculate the kinetic energy stored in an inertia element for different kinds of motions. You should be able to identify examples of inertias in real world systems. Student must be able to compute the equivalent inertia of elastic bars, torsional rods and beam configurations. Be able to calculate expression for equivalent inertias for systems with combined translational and rotational (torsional) elements. Student should be able to device one or more methods to measure the mass and mass moment of inertia of a mechanical element. Student should be proficient in the use of scales and calipers for measuring dimensions in a mechanical element.

2.        Student should be able to model the constitutive behavior of mechanical translational and rotational stiffness elements by relating the force or torque of the element to the displacement or angular deformation across the element. Calculate the potential (strain) energy stored in a stiffness. Student should be able to apply a consistent sign convention for forces (torques) and displacements (angular displacements) to a stiffness element. You should be able to identify examples of stiffnesses in real world systems. Student should be able to compute the equivalent stiffness of simple elastic bars, torsional rods and beam configurations. Be able to calculate an equivalent stiffness for systems with combined translational and rotational (torsional) elements. Student should be able to device one or more methods to identify the stiffness coefficient of an elastic element. You must be proficient in the appropriate use of calipers and dial gauges for measurements.

3.        Student should be able to model the constitutive behavior of a mechanical translational and rotational dampers by relating the velocity (angular) velocity across the damper to the force (torque) opposing the motion. Be able to discuss the different kinds of damping elements (viscous, Coulomb-type, aerodynamic, etc.) and their mechanism of energy dissipation. You should be able to calculate the power dissipated in a damper element. Demonstrate how to apply a consistent sign convention for forces (torques) and velocity to an damping element. You should be able to identify examples of damping (dissipative) elements in real world systems. Be able to calculate an equivalent damping coefficient for systems with combined translational and rotational (torsional) elements. Student should be able to device one or more methods to measure the forces (torques) associated with a dissipative mechanical element.

4.        Given a mechanical system, student should be able to create a system model consisting of lumped inertias, stiffnesses and damping elements, and external forcing functions. You should be able to identify constraints among the system elements and model them mathematically. Student should be able to discuss the advantages and disadvantages or limitations of the model in relationship with the actual "hardware".

5.        Given a nonlinear constitutive relationship for a dynamic lumped element, student should be able to determine a linear relationship that approximates the actual non-linearity for small motions in some neighborhood of an equilibrium state. You must be able to explain the purpose of linearization and how to determine the validity of the approximation within the context of system performance.

6.        Student should be able to explain fundamental mass flow relationships for fluidic systems. Be able to discuss the flow through orifices and valves, provide constitutive relationships between flow and pressure (head) and be able to linearize the action of non-linear flow elements around some equilibrium operating point.

7.        Given a mechanical system model of interconnected lumped inertias, stiffnesses and dampers, student should be able to determine the number of degrees-of-freedom (DOF) of the system and a set of independent coordinates describing the system motion. You must be able to identify the kinematic constraints between elements or sub- systems. You must be able to draw a complete free body diagram for each lumped element in the system, and uniquely identifying the interconnecting forces and moments associated to other lumped elements. Student must be able to use the principles of conservation of linear momentum (Newton's 2nd Law) or angular momentum, or the energy conservation principle to derive the differential equation(s) of motion describing the behavior of the mechanical system. Student must be able to identify the initial configuration of the system and translate this into initial values of displacements and velocities from which system motion will follow (see C below).

B.        Student should be able to mathematically model simple electrical circuits consisting of series and parallel arrangements of voltage and current sources, resistors, capacitors, and inductors.

1.        Student should be able to sketch the relationship between charge and voltage in a capacitor, determine the energy stored in a capacitor, and physically explain what a capacitor does.

2. Student should be able to sketch the general relationship between magnetic flux and current in an inductor, determine the energy stored in a inductor, and physically explain what an inductor does.

3.        Given a circuit, student should determine the number of independent currents (DOF) as coordinates with a sign convention. You must be able to determine constitutive relationships for each electrical element in terms of voltage drops and element currents. Student should identify sufficient nodes for balance of currents (Kirchoff's law) and write enough voltage loop equations for the number of DOFs in the system.

4.        Student should be able to describe the fundamental principle of operation of a DC (direct current) motor by explaining the transformation of electrical power into magnetic fluxes, and conversion to mechanical energy. You must be able to identify the differences between AC and DC motors. You should be able to write the fundamental coupled equations of motion for a DC motor driving a mechanical rotational element. Student should be able to discuss analogies between fundamental electrical system elements and those found in mechanical systems.

            Student should be able to operate efficiently instrumentation for measurement of electrical signals, i.e. voltmeters, oscilloscopes, and signal generators.

C.        Solution of 1st and 2nd order, linear ordinary differential equations with constant coefficients describing system dynamics. You should be able to take the single or sets of equations generated in objectives A and B and solve them to predict the time response, and relate the mathematical solutions to the physics of the problem.

1.        Student must be able to solve for the time response of a system described by a first order differential equation and subject to initials conditions. Student must be able to identify the most important characteristics of the system responses to impulse, step, ramp and periodic forcing functions (external excitations). You must be able to determine the characteristic equation of the system and evaluate the system time constant (t ). You should be able to relate the time constant to the physical parameters of the system and explain the importance of t on the system speed of response. You should be able to give physical examples of systems that behave predominately as first order systems. Describe how system parameters influence the time constant and explain ways to improve the system response by modification of the system parameters.

2.        Students must be able to solve for the time response of a system described by a 2nd order differential equation and subject to initial conditions. Student must be able to identify the most important characteristics of the system responses to impulse, step, ramp and periodic forcing functions (external excitations). You must be able to determine the characteristic system equation and evaluate the natural frequency (w n) and damping ratio (x ) in terms of the system parameters. Student should explain the concept of natural frequency and its importance on the response of the system. Be able to explain why a purely conservative system oscillates by using energy concepts. Evaluate the damping ratio (x ) in terms of system parameters and explain its effect on the amplitude and speed of response of the system. Establish necessary conditions on the system physical parameters for the system to be both statically and dynamically stable. You should be able to identify whether the system dynamics correspond to underdamped, critically damped or overdamped systems depending on the damping ratio. Be prepared to discuss the significance of these concepts. Explain the influence of system parameters and initial conditions on the dynamic response of the system for free and forced dynamic responses. Do initial conditions affect the frequency of response in a 2nd order system without external loading?. You should be able to give physical examples of systems that behave predominately as 2nd order systems. Describe how system parameters influence the performance measures such as natural frequency, damping ratio, and time constant. Student must explain the concepts of transient and steady state responses in terms of the external load excitations or initial conditions imposed on the system. You should be able to explain one or more methods to measure the damping coefficient in a 2nd order system. Explain how the logarithmic decrement is determined from experiments and indicate its importance and relationship to system damping.

D.       Solution and frequency response analysis of 1st and 2nd order linear systems. Student should be able to determine the dynamic response of a system subjected to external loads of periodic nature and determine the frequency response function (FRF) of the system.

1.        You must be able to find the transfer function of a first or second order system by relating the appropriate input and output to the system. Solve for the complex frequency response and determine the magnitude and phase of the frequency response in closed form and with asymptotic approximations. Explain the physical meaning of the frequency response. Explain a mechanical system design or analysis problem where frequency response is critical for its performance. Describe how the system parameters or natural frequency and damping ratio affect the system FRF. Do initial conditions affect the FRF of a system?. Explain the concept of Q-factor and its importance on the system dynamic performance. Establish the regimes of operation of a system below, close to, or above its natural frequency. Student should be able to draw diagrams of forces for each element in the system (inertia, stiffness and damper) and explain their role at the different regimes of operation (below, above or at the natural frequency). Explain the concept of force transmissibility and its importance on the life and operation of a mechanical system. Discuss methods or procedures to reduce the amplitude of oscillatory motion in a mechanical system at a particular operating frequency by modifying the system parameters.

E. Student must be able to linearize non-linear differential equations and demonstrate the validity of the procedure for small motions about an equilibrium point or state. You must be able to use computational methods such as Euler's scheme or average acceleration method to calculate the numerical solution of a second order non-linear differential equation. You should be able to explain the concepts of consistency, accuracy, and convergence of a numerical algorithm. Student should know the limitations of most numerical integrators in regard to the time step of integration.

Independent of the physical details of the system studied, the student should be able to answer the following questions:

a. How does the system respond with time for any particular type of disturbance ?

b. How long it will take for the dynamic action to dissipate if the disturbance is briefly applied and then removed ?

c. Whether the system is stable or if its oscillations will increase in magnitude with time even after the disturbance has been removed.

d. What modifications can be made to the system to improve its dynamic characteristics with regard to some specific application?

Prepared and modified by Dr. Luis San Andrés, August 18, 1998, July 22, 1997, August 1998, August 2000

Mechanical Engineering Department, Texas A&M University, College Station, TX 77843

 

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Appendix C

Syllabus for Mechanical Systems I Laboratory
Objectives and Policies, The Technical Memorandum
Introduction to Uncertainty Analysis

Dr. Luis San Andrés
Instructor Fall 2000
(Top)

Laboratory Objectives and Policies FALL 2000

Objectives:

1)       To demonstrate the desirability of making measurements whenever practical rather than relying solely on theory and computation.

2)       To account for typical discrepancies between theory and measurement in determining the values of mechanical system parameters.

3)       To provide some hands-on experience in making mechanical measurements.

4)       To provide some experience in modeling of mechanical systems using numerical simulations with a computer.

Laboratory Policies:

This policy gives guidelines in an attempt to maintain an equality of grading across sections. These guidelines are subject to reasonable modifications by the laboratory instructors to suit special conditions that may arise.

Report writing is more of an art than science. The students improve this skill by practice and by reading technical journal papers such as those found in the ASME Transactions, especially those reporting experimental measurements. Read the following material with detail to prepare your Technical Memos reporting the Laboratory practices and results.

OVERALL LAB GRADE:     Lab Report grade average (20%)

          Quizzes (5%), Pre-labs(5%) TOTAL 30% of CLASS GRADE

LAB REPORTS will be presented as TECHNICAL MEMORANDUMs (TM). The GRADE is determined primarily by the overall readability, impact and technical competence as judged by the laboratory instructor and teaching assistant. The following guidelines for evaluation have proven useful:

Neatness and English (correct, complete, concise)               30%

Accuracy of results                                         40%

Quality of discussion content                                    30%    TOTAL 100%

REFERENCES:

Writing Laboratory Reports in Mechanical Engineering, H.R. Thornton and M.J. Killingsworth, 1993, available at TEES Copy Center, WERC 221.

Experimentation and Uncertainty Analysis for Engineers, H. Coleman & W. Steele, Wiley Pubs, 1989

NOTES:

TM (Lab) #1 must include a detailed statistical analysis for the estimation of friction coefficients.

TM (Lab) #2 must include a detailed uncertainty analysis for the estimation of stiffness coefficients.

Statistical and uncertainty analyses are optional for other lab reports. If these are included, then bonus points up to 10% of Lab Report Grade will be awarded.

All calculated results and final measurements need to be presented in S.I. units with U.S. customary units in parentheses.

All data sheets must be originals in your handwriting and included as an Appendix in your Lab TM.

ATTENDANCE is expected except for University-approved excuses (letter from Dean’s office).

SCHOLASTIC HONESTY is expected not only in quiz taking, but also in recording your own data and writing your own report. Violations of the honor code will result in a zero grade followed by adherence to University Regulations regarding the violation.

LATE REPORTS will be graded with the following deductions:

                        10% of Report Grade for every day passed the due date,

                        15% of Report Grade for every weekend passed the due date.

You can download material related to the laboratory: syllabus, tech memo format, uncertainty analysis, and laboratory descriptions at http://metrib.tamu.edu/me334/labs.

TM: Technical Memorandum

LAB

Dates

Lecture Material (subject to revision)

Activity

Week

 

9/01

Laboratory objectives, description of grading and policies. Short review on physical units, statistics and uncertainty analysis

Lecture, handouts

1

1

9/08

Coulomb Friction Estimation of dry and lubricated friction coefficients from a block sliding in an inclined. (Statistical analysis required for Lab 1)

Quiz, Measurements

2

2

9/15

Mechanical Stiffness Measurement of structural stiffness coefficient for cantilever & built ends beams. Usage of force dial gauges and calibrated weights to measure beam (structural) deflections. (Uncertainty analysis required for Lab 2)

Quiz, Measurements, TM Lab 1 due

3

3

9/22

Mass properties Determination of a structure (pendulum) mass and mass moment of inertia about an axis using geometry, CG (first and second moment) principles and the natural motion of a bifilar pendulum.

Quiz, Measurements, TM Lab 2 due

4

4

9/29

Electrical Circuits and Filters Warm up using voltmeters and oscilloscopes. Build a R-C (resistor-capacitance) circuit (first order system) and measure its time constant. Introduction to use of oscilloscope and signal generators. Effect of excitation frequency on R-C system response.

Quiz, Measurements, TM Lab 3 due

5

 

10/06

NO LAB this week Oct. 7, Wed. 7-9 p.m.

EXAM I

6

5

10/13

DC Electric Motors Identification of motor constant and use of power relations at steady state. Measurement of DC motor resistance and inductance, and estimation of rotor inertia. Identification of drag torque as motor speed increases.

Quiz, Measurements, TM Lab 4 due

7

6

10/20

Free Vibrations Measurement of natural frequency and logarithmic decrement (damping ratio) in a vibrating cantilever beam. Use of piezoelectric accelerometers

Quiz, Measurements, TM Lab 5 due

8

7

10/27

Free Vibrations of Nonlinear pendulum and A/D data acquisition Measurement of free response of an oscillating pendulum. Introduction to analog/digital data acquisition with a computer.

Quiz, Measurements, TM 5 & 6 due

9

8

11/03

Numerical Simulation of Nonlinear System Review of numerical methods for solution of ODE’s. Applications to large motions of an oscillating pendulum

Quiz, Measurements, TM Lab 7 due

10

 

11/10

NO LAB this week Nov. 11, Wed. 7-9 p.m.

EXAM II

11

9

11/17

Frequency Response Measurement of the dynamic response of a cantilever beam due to periodic forcing. Prediction of maximum amplitude response and critical speed. Demonstration on use of frequency analyzer.

Quiz, Measurements, TM Lab 8 due

12

 

11/24

NO LAB this week Thanksgiving Nov. 26th

 

13

10

12/01

Turboelectric Drive Train Dynamic response of a first order system and measurement of coast down response. Identification of system time constant and measurement of system inertia and drag coefficient.

Quiz, Measurements, TM Lab 9 due

14

 

12/08

Last day of class Tuesday 12/08

TM Lab10 due

15

 

12/14

501-502-503: Mon. Dec. 15, 1:00-3:00 p.m. ZACH 127B

Final Exam

16

                                               

MEEN 334: Laboratory Report Format

                                                                                   

To:           MEEN 334 Students

From:      MEEN 334 laboratory Coordinator

Subject:   Writing Technical memos for meEN 334

Date:        September 1, 1998

SUMMARY OF THIS MEMO
This memorandum explains (and demonstrates) how to write a technical memorandum (TM). Webster’s defines a memorandum as a "usually brief communication written for interoffice circulation . . . a communication that contains directive, advisory, or informative matter". Adding the adjective "technical" implies a certain degree of structure both in format and content. A TM is a concise and well written communication approximately three to six pages long that:

  1. defines a task,
  2. specifies the objectives of the task,
  3. identifies and outlines a solution method and/or an experimental procedure,
  4. reports and discusses the results of implementing the solution and/or the estimated parameters from the measurements, and
  5. states conclusions and provides recommendations.

It is often necessary to include an informal appendix (sometimes handwritten) containing the data, sample calculations, etc. to support statements made in 4 and 5. Descriptions of the various parts of a TM follow.


HEADING
Your heading should follow the format of this memo. Your memo must be dated. (All correspondence, analysis, etc. should be dated.) The heading of a memo contains parts for "TO", "FROM", and "SUBJECT". The TO part identifies the recipient of the memo by name and title; for memos reporting on 334 labs the recipient is the teaching assistant who teaches you lab. The FROM part identifies you by name and course/section number; e.g., Joe Studious, ME 334.501 (or Jane Graduated, Principal Engineer, Old Ags Corp.). Sign the memo. The SUBJECT part is equivalent to a title and tells what the memo is about as completely and concisely as possible.

PURPOSE/SUMMARY
Concisely define the task in terms of the objectives of the laboratory practice and specify any restrictions/constraints. Summarize the major findings, conclusions and difficulties found. Sound engineering practice demands a very precise usage of technical terms and short sentence structure. Do not state the pedagogical objectives! This is not an introduction; do not give a lot of background and motivation. For 334 Lab the reader is the lab TA; he is your boss. If he assigned you this project, you do not need to explain to him why you are doing it. You must explain exactly what you are going to do, but you do not need to give the motivation for the project. (The total length of this section should not exceed 200 words).

METHOD
Describe the method you used to solve the problem (theoretical, experimental, or both) including any major assumptions, important equations, and/or experimental procedures. Describe the physical set-up where you performed the practice. Describe the type of instrumentation used and whether this is adequate for the task at hand.

This section almost always requires some sketches or drawings, i.e. figures. Figures should be referred in the text in ascending number and accompanied by meaningful and explanatory captions. Note that lengthy derivations of equations and too detailed descriptions of experimental procedures should be moved to an appendix.

PROCEDURE
Here you must describe in a logical manner the procedures and the type of measurements (static, dynamic, or both) you performed. Indicate the number of measurements taken and whether the values recorded are repeatable and consistent with each other.

RESULTS and DISCUSSION
All results are to be presented in the units of actual measurement or calculation, either English or SI, with final values in alternative units given in parenthesis.

Present the measured data in a form best suited to help the reader understand their significance in light of the stated objectives. This will usually be graphs or curves, supplemented by tables highlighting identified (measured) or calculated values.

Present all of the significant findings of the study and explain any important observations, trends, or limitations. Discuss how these observations (measurements) will lead to your final and important conclusions, and how well (or not) the identified parameters from the experiments compare to analytical results. Make sure you address here ALL the questions posed on your Lab Form under the heading IMPORTANT QUESTIONS

This section must also contain either the final results of your (1) a statistical analysis of the data, i.e. average or mean values and standard deviations, or (2) overall values of experimental uncertainty, and/or (3) an explanation of discarded data. (where applicable).

CONCLUSIONS
Always state your conclusions. Conclusion must address the purpose of the project as stated in the first paragraph of the TM. Some students (and professionals) do not want to risk making erroneous conclusion so they waffle on stating conclusions. For example, they may list several possible conclusions, but leave it up to the reader to choose one. You did not spend five years of your life studying engineering so that you could collect data and present it. You are educated and qualified to analyze the data and draw conclusions from it. Your boss thinks enough of your qualifications to pay you a good salary, and he expects conclusions and sound recommendations. The only exception is the case in which the data does not support a conclusion; and in this exceptional case, the method used is inadequate for the purpose and you should so state.

APPENDICES
Appendix A must always contain at least one data sheet, the one you wrote your experimental observations and measurements while at the practice. Additional appendices (B, C, etc.) can contain repetitive calculations, copies of referenced material, etc. Lengthy calculations should be included as an Appendix. Here you show how all your calculations are made, including physical units. Avoid unnecessary repetitions of calculations.

 

MEEN 334: Introduction to Uncertainty Analysis

Adapted from Experimentation and Uncertainty Analysis for Engineers, H. Coleman & W. Steele, Wiley Pubs, 1989

In many cases we do not measure directly the value of an experimental result. Instead, we measure the values of several variable s or parameters and combine them in a data reduction equation to obtain the desired result.

For example, consider and experiment to answer the question:

"What is the density of air in a pressurized tank?"

Not having a density meter, we have to resort to physical principles and determine the density indirectly by using (one way of doing it) the equation of state of an ideal gas, i.e.,

                (1)

If we know the gas constant R and if we can measure the gas pressure (P) and absolute temperature (T) within the tank then we can estimate a value of the gas density (r ).

The measurements of each of the variables (P,T) have uncertainties associated with them, as well as the tabulated values of material properties (R) taken from references.

The key question in experimentation is:

How do the uncertainties in the individual variables propagate through a data reduction equation into a final (estimated) result?

The answer is obtained by using UNCERTAINTY ANALYSIS

Here we consider only the general or overall measurement uncertainties and not the details of the bias and precision (accuracy components). This is generally done on the planning phase of the experimentation.

An experimental result, say j , is a function of the set of variables xi . This can be described in the general functional form:

                       (2)

Equation (2) is the one used to determine j from the measured variables. The uncertainty in the result is then given by:

                             (3)

where Uxi are the uncertainties associated to the measured variables xi and the partial derivatives are defined as "absolute sensitivity coefficients." The following rules of thumb have been proven to be useful in uncertainty analysis.

RULE #1: Always solve the data equation for the experimental result before performing an uncertainty analysis, i.e., if we want to find the density by measuring (P,T), then r = P/RT and

and calculating the derivatives:

RULE #2: Always try to divide the uncertainty expression Uj by the experimental result j to see if algebraic simplification is possible, i.e., from (b) we can easily see that since r = P/RT:

For this example, UR is negligible (assumed zero) since the uncertainty in a universal constant is much less than the others, i.e., its measurement is performed with the greatest accuracy.

Example I

A pressurized air tank is nominally at ambient temperature (25° C). How accurately can the air density be determined if the temperature is measured with an uncertainty of 1° C and the tank pressure is measured with an uncertainty of 3%. From the data we have:

then, since UR = 0

In this example, the uncertainty in the measurement of pressure dominates the estimation of the gas density. If the end result renders a too large uncertainty for the parameter of interest (density), then it indicates the need to procure a method (and instrumentation) to measure the gas pressure more accurately.

 

Example II:

Consider the calculation of electric power from

          P = E x l

where E and I are measured as

          E = 100 volts ± 2 volts

          l = 10 amp ± 0.3 amp

The nominal value of the power is P=100 x 10 = 1,000 watts. By taking the worst possible variations in voltage and current, we could calculate

          Pmax = (100 + 2)(10 + 0.3) = 1050.6 watts

         

          Pmin = (100 - 2)(10 - 0.3) = 950.6 watts

Thus, using a simple method of calculation, i.e. (Pmax-P)/P, the difference (error) in the power is +5.06 %, -4.94 % for Pmax and Pmin, respectively. It is quite unlikely that the power would be in error by these amounts because the voltmeter variations would probably not correspond with the ammeter variations. When the voltmeter reads an extreme "high," there is no reason why the ammeter must also read an extreme "high" at that particular instant; indeed, this combination is most unlikely.

The simple calculation applied to the electric-power equation above is a useful way of inspecting experimental data to determine what error could result in a final calculation; however, the test is too severe and should be used only for rough inspections of data.

Note however that the uncertainties in the measurement of current and voltage are equal to UI=0.3 A. and UE=2 volts, respectively. Hence, the uncertainty in the estimation (measurement) of the power is equal to:

UP/P = [ (UE/E)2 + (UI/I)2 ]1/2 = [ (0.02)2 + (0.03)2 ]1/2 = 0.036, i.e. 3.6% of the measured value.

NOTES:

  • The uncertainty value Uj is always a positive number (>0) with identical physical dimensions as the measured result j .
  • ASME Standards require [Uj /j ] < 0.05 (5%) for 95% coverage, i.e. uncertainty values larger than 5% of the measured value are discarded (unacceptable) in engineering practice.

 

MEEN 334: Review of Statistics

Mean Values:

The arithmetic mean of a set of n measurements {y1, y2, . . . ., yn } of a variable y is the sum of the measurements divided by the total number of measurements.

Important notes

  1. The mean is the arithmetic average of the measurements in data set.
  2. There is only one mean for a data set.
  3. The mean is, in some sense, the best estimate of the true value of y.
  4. The value of the mean is influenced by extreme measurements, trimming can help reduce the degree of influence.

Variance

The variance s2 of a set of n measurements {y1, y2, . . . ., yn } with mean is the sum of the square deviations, y i - , divided by (n - 1), i.e.

Standard Deviation

The standard deviations s of a set of measurements is the positive square root of the variance. The standard deviation is a measure of the tendency of the measurements to cluster about the mean value.

Empirical Rule

Give a set of n measurements possessing a mound-shaped histogram (Gaussian distribution about the mean value), then

          the interval ± s contains approximately 68% of the measurements, then

          the interval ± 2s contains approximately 95% of the measurements, and

          the interval ± 3s contains nearly all the measurements.

 

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Appendix D

Pictures of in-class demonstration kits
Dr. Luis San Andrés
Instructor
(Top)

NOT AVAILABLE  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix E

Ratings from student evaluation forms for
Dr. Luis San Andrés, Class Instructor
(Top)

The students reply to the following ten questions. A score of five (5) gives the highest rating while one (1) indicates the lowest.

  1. Lecture preparation: lectures are consistently well prepared and organized
  2. Assignments: course requirements, assignments, projects, etc, aid course objectives and are fair and evenly distributed.
  3. Communication: the instructor clearly explains material to a group.
  4. Responsiveness: the instructor is open to students’ questions and effectively answers them.
  5. Academic concern: the instructor seems to care whether the students learned.
  6. Availability: the instructor willingly makes time to help students.
  7. The instructor is fair and consistent in evaluating student performance.
  8. Environment: the instructor maintained a good learning environment in the lass.
  9. All things considered, this was a good course.
  10. All things considered: the instructor was an effective teacher.

New student evaluation forms where introduced in the fall semester 1998. These have twelve questions and with a similar rating scheme.

 Class: Mechanical Vibrations, MEEN 617 (graduate level)

Semester

mean

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

FA 90

4.21

4.5

4.21

3.79

4.64

4.29

3.57

3.86

4.14

4.5

3.93

FA 91

4.42

4.25

4.62

4.15

4.46

3.85

4.23

4.54

4.62

4.69

4.15

FA 93

4.62

4.53

4.65

4.29

4.41

4.47

4.59

4.18

4.71

4.76

4.47

SP 96

4.43

4.71

4

4.29

4.36

4.5

4.14

4.21

4.36

4.5

4.43

SP 97

4.8

4.46

4.5

4.46

4.5

4.38

4.42

4.75

4.67

4.5

4.8

AVERAGE

4.50

4.49

4.40

4.20

4.47

4.30

4.19

4.31

4.50

4.59

4.36

Class: Lubrication Theory, MEEN 626 (graduate level)

Semester

mean

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

SP 93

4.75

4.67

4.83

4.33

4.5

4.83

4.83

4.5

4.83

4.83

4.67

FA 95

4.85

4.77

4.54

4.92

4.85

4.85

4.85

4.77

4.69

5

4.85

FA 97

4.92

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

AVERAGE

4.84

4.72

4.68

4.62

4.67

4.84

4.84

4.63

4.76

4.91

4.76

 

Class: Mechanical Systems I, MEEN 334 (undergraduate level)

Semester

section

mean

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

SP 91

504

3.62

3.29

3.67

3.33

3.38

3.42

3.71

3.29

3.54

3.96

3.29

SP92

501

3.9

4.07

3.93

3.6

3.67

3.6

3.73

3.67

4

4.07

3.73

 

502

4.15

4.1

4.2

3.9

3.9

3.3

3.8

3.8

4.3

4.3

4

 

503

4

4.1

4.1

3.8

4.3

3.6

4.4

3.1

4

4.1

3.9

 

507

3.69

4.38

3.92

3.31

3.54

3.46

4

3.31

4

3.85

3.54

SP92

ALL

3.93

4.16

4.04

3.65

3.85

3.49

3.98

3.47

4.07

4.08

3.79

FA 92

505

4

 

 

 

 

 

 

 

 

 

 

SP 94

504

3.94

4.16

4.24

3.96

3.71

3.78

3.78

3.68

3.9

4.04

3.84

FA 94

505

3.95

4.25

4.14

4

3.85

3.93

3.86

3.82

4.14

3.96

3.93

FA 96

504

3.33

4.33

4

3.57

2.86

3.14

2.52

3.71

3.62

3.38

3.33

FA 97

501

4.49

 

 

 

 

 

 

 

 

 

 

 

AVERAGE

3.91

4.09

4.03

3.68

3.67

3.52

3.75

3.53

3.95

3.97

3.71

In the fall semester (1999) modified student evaluations were introduced with twelve questions.

section

mean

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

Q12

501

3.72

3.55

3.45

3.91

4.18

3.45

3.73

4.45

4

3.64

3.64

3.64

3.00

503

3.68

4.21

3.62

3.43

3.86

3.71

3.86

4.07

3.79

3.64

3.5

3.29

3.14

504

3.90

4.41

3.69

3.56

3.33

3.85

3.44

3.95

3.9

4.36

4.23

3.77

4.26

505

3.66

4.05

3.48

3.29

3.19

3.48

3.24

3.62

3.43

4.19

4.38

3.9

3.71

506

3.88

4.11

4.11

3.78

4.11

3.56

3.78

4.56

4.22

3.78

3.78

3.56

3.22

Average

3.76

4.07

3.67

3.59

3.73

3.61

3.61

4.13

3.87

3.92

3.91

3.63

3.47

Class: Modeling and Behavior of Engineering Systems, ENGR 203 (undergraduate level), spring 1995

section

mean

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

501

3.462

3.43

3.81

3.19

3

3.62

4.19

3.48

3.38

3.52

3

502

4.25

4.1

4.1

4.2

4

4.4

4.8

4.2

3.9

4.6

4.2

503

3.326

3.17

3.67

3

3.42

3.17

3.58

3.5

3.58

3.17

3

AVERAGE

3.68

3.57

3.86

3.46

3.47

3.73

4.19

3.73

3.62

3.73

3.4

 

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