MEEN 617 -
Mechanical Vibrations – SPRING 2008
Dr. Luis San Andrés
Last update:
April 11, 2008, assumed modes
method – Handwritten notes,
HD 15 –
Identification of parameters in mechanical systems
March 28, 2008, HD 13 Numerical integration MDOF systems
March 21, 2008: handout 14 vibes of continuum systems +
addendum to HD 9
March 17, 2008: handout 9
evaluation of eigenvalues
March 3, 2008: handouts
(6,7,8,11), Issues with FRF
January
23, 2008 (handout 4 & 10-vibration absorber)
January 16, 2008 (handouts 2c, 2d, recommended problems from
textbook
Course Description: Linear Theory of vibrations of Single and Multiple degree of freedom (DOF)
systems via Newtonian and Lagrangian formulations, and with emphasis on
analytical methods and computer applications. Prerequisites: MEEN 364,
MATH 308.
OBJECTIVES: To provide the fundamental analytical and numerical tools for analysis and modeling of vibration phenomena in discrete and continuum SDOF and MDOF linear systems. Learning of advanced analytical tools and methods for experimental identification of system parameters using recorded data, i.e. frequency domain parameter identification methods.
Class Time: T, R 2:20 – 3:35 pm, ZACH
119D
Instructor:
Dr. Luis San Andrés, ENPH 118, Phones :
862 4744, LsanAndres@Mengr.tamu.edu
Office hours: T, R 10:-11:00 am, or by scheduled appointment (phone call or e-mail in
advance).
References: Mechanical and Structural Vibration: Theory and
Applications, J. H. Ginsberg
Recommended problems from your textbook
|
week |
chapter |
Problem numbers |
|
1 |
1 |
5, 8, 13, 14, 15, 20, 43, 44, 56 |
|
2 |
2 |
|
|
3&4 |
3 |
3, 7, 19, 20, 22, 25, 50, 52 |
|
5 |
1 |
Derive EOMs MODF systems: 25, 27, 30, 33, 36, 38, 39, 44, 49 |
|
6 |
4 |
10/19, 21, 30, 36, 39,34, 55 |
|
7 |
5 |
14, 18, 29 |
|
8 |
7 |
3, 11, 43, 49 |
|
10 |
6 |
3, 9, 11, 14, 15, 28, 38, 54 |
NEW release in 2008 - Spring
Class Notes (handouts)
NEW Introduction
to the analysis of vibrations in mechanical systems.
Introduction to motion in mechanical systems. Definition of design, analysis, and testing. Steps in Modeling. Continuous and lumped parameter systems. Second Order Systems and differential equations of motion. Definitions of Free and Forced Responses. The purpose of analysis and the relevant issues to resolve.
1.
NEW Handout 1 Modeling of mechanical (lumped parameter) elements
Fundamental elements in mechanical
systems: inertias, stiffness and damping elements. 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).
NEW Appendix
A. Equivalence of principles of conservation of
mechanical energy and conservation of linear momentum.
NEW Appendix B.
Linearization
NEW Appendix C.
Derivation of
equations of motion for a multiple degree of freedom system
NEW Appendix
D. Note
on assumed modes
NEW Appendix
E. Vibration
sensors and their applications
2.
Dynamic response of second
order mechanical systems
NEW Handout
2a Free
response to initial conditions: viscous and coulomb damping systems. Forced response:
impulse and step loads.
NEW Handout 2b Periodic forced response and
Frequency response function of second order systems.
NEW Handout 2c Interpretation of forced
periodic response. Transmissibility (forces transmitted to base or foundation).
Frequency Response due
to base or foundation motions
NEW Handout 2d Fourier series. Forced
response to a periodic forced excitation. Response to a unit impulse.
Convolution integral and response to arbitrary loading (7 pages).
NEW Uses of the FRF on the design of mechanical
systems
4.
NEW Handout 4: Elements of analytical dynamics.
Work and
Energy – Single particle. Constraints – degrees of freedom. Principle of
virtual work. D’Alembert Principle.
5.
EXAMPLES:
Solutions to a
bunch of 1_DOF problems: derivation of Equations of Motion and Initial
Conditions in Simple Mechanical Systems, Free and Forced Responses, Frequency
response Functions
(distributed via e-mail to students
registered in class)
6.
NEW Numerical
solution of EOM for a single degree of freedom (SDOF) system. ().
Vibrations of multiple degree of freedom (MDOF) systems
7.
NEW Undamped
Modal Analysis of MDOF systems: Free & Force Vibrations of undamped MDOF
systems. Orthogonality properties of natural modes. Rayleigh energy methods.
Mode superposition
(displacement and acceleration methods)
8.
NEW Modal Analysis of
MDOF systems with Proportional Damping.
NEW Addendum: Mode
acceleration method
9.
NEW Numerical evaluation
of natural modes and frequencies. ().
10.
NEW The dynamic vibration
absorber (11 p).
11.
NEW Modal Analysis
of MDOF Systems with Viscous Damping (10 pages).
12.
Finite
element modeling of mechanical systems (OLD).
13.
NEW Numerical
methods for the dynamic response of MDOF damped systems ().
14.
NEW Dynamic
response of continuum systems ().
OLD:
Rayleigh-Ritz energy Methods (assumed modes
method) – Handwritten notes
15.
NEW Identification of parameters
in mechanical systems
The handouts and textbook 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.
Send all comments or questions to LsanAndres@Mengr.tamu.edu