ME 6442: Vibration of Mechanical
Systems
Offered Every Spring
Introductory course suitable for all research areas
| Credit
Hours: |
3-0-3 |
| Prerequisites:
|
ME
3015 and ME 3201 |
| Catalog
Description: |
Introduction
to modeling and oscillatory response analysis for discrete and continuous
mechanical and structural systems. |
| Textbook:
|
Jerry
H. Ginsberg; Mechanical and Structural
Vibrations: Theory and Applications, 1st Edition, John Wiley, 2001. |
| Instructors:
|
Kenneth
Cunefare, Aldo Ferri, and Jerry Ginsberg (Spring 2004) |
Topics:
- Equations of
motion: Review of dynamics of planar motion, introduction to Lagrange's
equations, linearization, lumped system parameters, inertial and stiffness
coupling, numerical methods for differential equations of motion.
- Linear vibration
of a single degree of freedom systems with damping: free vibration, Coulomb
friction, response to harmonic excitation, beating and resonant response,
Fourier series solution for periodic excitation, transient response by
superposition, convolution integrals, numerical methods, application of
FFT algorithms.
- Free motion
of undamped multiple degree of freedom systems: General equations of motion,
formulations using stiffness or flexibility matrix, eigenvalue problem
for natural frequencies and modes, application of numerical methods, rigid
body modes and repeated frequencies, orthogonality of modes.
- Forced response
of undamped multiple degree of freedom systems: modal analysis - principal
coordinates and uncoupled equations, response to initial conditions, steady-state
response to harmonic excitation, vibration absorbers, transient response.
- Damping in multiple
degree of freedom systems: modal analysis for proportional and light damping,
frequency domain transfer functions, vibration absorbers, application of
FFT's for transient response, damped modes in the state-space, modal analysis
using damped modes.
- Continuous systems
by the Ritz method: Hamilton's principle for extensional and flexural deformation
of bars, geometric and natural boundary conditions, elastic and inertial
attachments, basis functions for Ritz series, discretized equations, natural
frequencies and displacement mode shapes, orthogonality, forced response,
time-dependent boundary conditions
- Topics selected
from: response of gyroscopic systems, dynamic stability of beams, pipes
with ineternal fluid flow, and rotating shafts, random vibrations, basic
concepts for finite element analysis, nonlinear vibration of single-degree-of
freedom systems
Grading: Midterm
(30%), final (30%), Project (20%), HW (20%)
_____________________
Revised June 2004