Teaching
Portfolio
Luis A.
San Andrés, Professor
Mechanical Engineering
Department,
February 2005
Appendix B. Performance Objectives
for Mechanical Systems I class 
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,
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, selfmotivated 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:
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
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
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:
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,
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, takehome 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).
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 noncheating
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
handsonexperience 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 selfcontained 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 demokits
include simple massspringdamper systems (1 and 2DOF), 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:
In
addition to these ten questions, the students also provide valuable written
comments and feedback related to the following questions:
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 extracredit opportunities. Tried to relate reallife 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 AfroAmerican). 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+ coauthored 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 

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, “BumpType Foil Bearing Structural Stiffness: Experiments and
Predictions”, ASME Paper GT 200553611 (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 OilFree
Turbomachinery,” ASME Paper GT 200338833, ASME TurboExpo 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:
I believe that my role as a
graduate student advisor to the potential MS or Ph.D. candidate includes:
On the other hand, I believe my
role as an advisor does not include the following activities,
I expect from a graduate student
performing research under my direction:
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
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.
MOVE
TO (Top) of document
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 
8450160, LsanAndres@Mengr.tamu.edu
Office hours: T:
Class Time: 501/502/503, T,R
Labs: 501  T 2:
References: System Dynamics, an Introduction, D. Rowell and D. Wormley,
Prentice Hall Pubs, 1997.
MEEN 334 Class Notes (handouts),
L. San Andrés,
MEEN
Laboratory Manual (URL sites phased out – not public access)
Other: Dynamics of Physical
Systems, R. H. Cannon, McGrawHill Pub. Co, 1967.
Analysis and Design of Dynamic Systems,
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
Mechanical Vibrations, S.S. Rao,
AddisonWesley Pubs., 2^{nd} Ed., 1990.
EXAM SCHEDULE: 1: Physical & Mathematical Modeling, Wed.,
Oct. 7,
2: Dynamic Response of Systems, Wed.,
Nov. 11,
3: Final Comprehensive Exam, 501/502/503, Mon., Dec. 14,1:
Grading: Practice problems assigned but not graded.
GRADED group takehome quizzes every Tuesday and turned in on Thursday. Two inclass exams and a comprehensive final exam. Exams
will cover the material specified in the Meen 334 PERFORMANCE
OBJECTIVES. No makeup 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
email] 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. 114 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. 1937 
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.120145, 
4 
9/21 
Equations
of motion in mechanical systems Constraints and Degrees of Freedom. Free
response (due to initial conditions) of massspring oscillator  The concept
of harmonic motions and natural frequency . Linearization
of nonlinear mechanical systems. 
HD #5:
Examples Chp. 3, pp. 8389 
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. 3744, 4453, 5359 
6 
10/05 
Review
Oct. 7, Wed. 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. 276294, 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. 309320, 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. 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.453472 
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. 26^{th} 
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 
501502503:
Mon., Dec. 14, 
ZACH 127B,
FINAL EXAM 
Important note, Chapter
8.3: Classical solution of linear differential equations is responsibility
of student.
Policies Meen 334  Mechanical Systems
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, inclass 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.
Takehome 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
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
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 emails for communication with your instructor
is acceptable. I usually receive three types of email messages:
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. Xcopies 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 oneport 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.
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
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:
AND LAST BUT
NOT LEAST: DESIRE AND WILL TO LEARN !!
See a full description of Performance
Objectives at class URL site
GLOBAL
PERFORMANCE OBJECTIVES
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
0. Cover and Index ( 2 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)
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 electromagnetic
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.
a)
Free
response to initial conditions: Systems with dryfriction and viscous damping.
b) Forced response: step, ramp and periodic loads.
c) Frequency response function of first order
systems: response to periodic loading.
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) Xcopies only.
Move
to (Top) of document
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
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
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
nonlinear 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,
Coulombtype, 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 nonlinearity 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 nonlinear
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 degreesoffreedom (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 (
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 Qfactor 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 nonlinear 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 nonlinear 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,
Mechanical
Engineering Department,
Move to (Top)
Document
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 handson 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%), Prelabs(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
All data sheets
must be originals in your handwriting and included as an Appendix in your Lab
TM.
ATTENDANCE is expected except for
Universityapproved 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 RC
(resistorcapacitance) circuit (first order system) and measure its time
constant. Introduction to use of oscilloscope and signal generators. Effect
of excitation frequency on RC system response. 
Quiz, Measurements, TM Lab
3 due 
5 

10/06 
NO LAB this week Oct. 7, Wed. 
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. 
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 
501502503: Mon. Dec. 15, 
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:
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
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 setup 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 x_{i} . 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 U_{xi}_{
}are the uncertainties associated to the measured variables x_{i} 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,
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
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
P_{max} = (100 + 2)(10
+ 0.3) = 1050.6 watts
P_{min} = (100  2)(10
 0.3) = 950.6 watts
Thus, using a simple method of
calculation, i.e. (P_{max}P)/P, the
difference (error) in the power is +5.06 %, 4.94 % for P_{max}
and P_{min}, 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 electricpower 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 U_{I}=0.3
A. and U_{E}=2 volts, respectively. Hence, the uncertainty in
the estimation (measurement) of the power is equal to:
U_{P}/P = [ (U_{E}/E)^{2}
+ (U_{I}/I)^{2} ]^{1/2} = [ (0.02)^{2} + (0.03)^{2}
]^{1/2 }= 0.036, i.e. 3.6% of the measured value.
NOTES:
MEEN 334:
Review of Statistics
Mean Values:
The arithmetic mean of a set of n measurements {y_{1, }y_{2, . . . .,}
y_{n} } of a variable y is the sum
of the measurements divided by the total number of measurements.
Important notes
Variance
The variance s^{2 }of
a set of n measurements {y_{1, }y_{2, . . . .,} y_{n}_{
}} 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 moundshaped 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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Pictures of inclass demonstration kits
Dr. Luis San Andrés
Instructor
(Top)
NOT AVAILABLE
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.
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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