Dynamics and Vibrations
PERFORMANCE
OBJECTIVES or OUTCOMES
WHAT YOU WILL LEARN IN THIS COURSE & WHERE YOU WILL
APPLY IT
Planar kinematics for particle motion:
Student should be able to use Cartesian, polar and path-coordinate kinematics
to define the velocity and acceleration components of a material point in
motion. Student will learn to use
coordinate transformations to shift back and forth between the three coordinate
systems (Cartesian, polar and path). Student should be able to mathematically
differentiate functions of time and space coordinates to determine desired
functional forms.
Physical
modeling of particle dynamics (1 DOF): You should be able to identify the
fundamental components of mechanical systems into generalized lumped mass
(inertia) M, stiffness K, damping C 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. You should be
able to derive the fundamental equations governing the motion of
lumped-parameter (1 DOF and 2 DOF) 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.
Mathematical
modeling of 1 DOF mechanical systems: Student should be able to determine
analytically the dynamic response (Solutions) of 1DOF systems described by the
linear ODE 
and given initial conditions. Be able to explain the
concept of natural frequency wn. Determine the free (transient) response
to initial conditions and the dynamic response to Impulse and Step loads. Be
able to discuss the concepts of transient and steady state responses,
and the effect of viscous damping ratio (and logarithmic decrement) on the
amplitude and decay speed of system response.
Derive the dynamic response to periodic (harmonic) external forcing
functions and discuss about the regimes of operation: below, close to, or above
its natural frequency. Be able to obtain the Frequency Response Function (FRF)
for sustained periodic excitations and explain the effects of system parameters
and frequency on the Amplitude of motion and Phase lag. Use FRF for appropriate design considerations
and reliable operation of vibrating systems.
Mathematical
modeling of 2 DOF mechanical systems:
Student should be able to derive the EOMS for 2- or M-DOF lumped
parameter systems. You should be able to linearize the EOMs about an
equilibrium or operating point and determine the linear system of ODEs: 
. For undamped 2-DOF systems Student should be able to
determine analytically the eigenvalues and eigenvectors of 
. Be able to explain the concept of modal (natural)
coordinates and mode shapes. Student should be able to use the transformation 
to uncouple the EOMS
in physical coordinates and determine (analytically) the free and forced response
of 2-DOF systems to arbitrary initial conditions, step and periodic loads.
Numerical
modeling of mechanical systems: Student should be able to
use computational software to solve linear and nonlinear algebraic and
differential equations describing the motion of 1- or M-DOF systems. You should
be able to apply knowledge gained in MEEN 357 to select appropriate numerical
techniques with due consideration for time steps and procedures (algorithms)
ensuring accurate, numerically stable, and cost efficient system response.
Student should be able to interpret numerical calculations (predictions) to
explain system behavior (motion), identify possible failure mechanisms due to
excessive amplitudes of motion or reaction forces, etc.
Luis
San Andrés
Course
Instructor