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L/R 321. Vibrations of Mechanical Systems.
Analysis of transient and steady motion of single and multi-degree
of freedom linear and non-linear systems. The
course will involve both analytical solution techniques for linear
systems and numerical simulations using computer
modeling. Application to vehicle dynamics and seismic loading of structures
will be considered.
| Week | CORE TOPICS (Reading assignments: Thompson) |
| 1 | Periodic Motion, Simple Harmonic Motion, Fourier Series,
Kinematics of Vibrations (Chapter 1). |
| 2 | Damped Free Vibrations with One Degree of Freedom: Mass-Spring System,
Torsional and Compound Pendulums (Sections 2.1 - 2.3). |
| 3 | Energy Methods, Rayleigh Method of Effective Mass, Virtual Work, Viscously
Damped Free Vibrations, Coulomb Damping (Sections 2.4 - 2.8). |
| 4 | Forced Harmonic Vibrations, Rotating Unbalance, Rotor Unbalance,
Rotating Shafts, Support Motion (Sections 3.1 - 3.5). |
| 5 | Vibration Isolation, Energy Disspation by Damping, Viscous Damping
Strutural Damping (Sections 3.6 - 3.11). |
| 6 | Transient Vibration, Impulse Excitation, Arbitrary Excitation,
Laplace Transform Methods (Sections 4.1 - 4.3) |
| 7 | Pulse Excitation and Rise Time, Shock Response, Shock Isolation,
Numerical Cumputations (Sections 4.4 - 4.7). |
| 8 | Systems with Many Degrees of Freedom, Normal Modes and Coordinate Coupling
Initial Conditions (Sections 5.1 - 5.2). |
| 9 | Coordinate Coupling, Static and Dynamic Coupling, Forced Harmonic
Vibration, Centrifugal Pendulum Vibrator Absorber (Sections 5.3 - 5.4 and 5.7). |
| 10 | More on Vibrating Systems, Flexibility Influence Coefficients, Reciprocity
Theorem, Stifness influence Coefficients (Sections 6.1 - 6.3). |
| 11 | Eigenvalues, Eigenvectors, Diagonalization, Orthgonality (Sections 6.6 - 6.12). |
| 12 | Generalized Coordinates, Virtual Work, Lagrange's Equations (Sections 7.1 - 7.3). |
| 13 | Kinetic Energy, Potential Energy, Generalized Forces (Sections 7.4 - 7.5). |
| 14 | The Methods of Rayleigh and Ritz, Dunkerley's Equation, Holzer's Method
(Sections 12.1 - 12.4) |
| 15 | Final Exam |
Updated 1/15/02.
2. Academic Integrity: Students are encouraged to help each other to learn by discussion and demonstrations of general ideas, concepts and techniques. You must accept responsibility for distinguishing between legitimate academic discussion and plagiarism. Collegiality is encouraged; however, the final version of each assignment must be the work of the individual student, except where teamwork is explicitly acknowledged at the top of the document handed in. It is also your responsibility to recognize sources of information by means of appropriate reference notes.
3. Form and Completeness of Work: Remember that work handed in by you has to be read and evaluated by a Professor or a Course Assistant. Common courtesy requires that you indicate clearly the lines of reasoning used in your work. Just giving the answer is not sufficient. The grader has got to be assured that your reasoning is correct. At a bare minimum every assignment should have careful statements of the following:
What is GIVEN:
What is REQUIRED:
SOLUTION details:
ANSWERS: (clearly identified)
In addition, most problems will also require Sketches, Plots, and diagrams. You should also include Computer program listings and outputs, when used, and be sure to indicate the source of the programs (your own creation, or from a public source).
4. MATLAB: The use of MATLAB is strongly encouraged
as a learning aid in this course. This “language” is ideally suited
to work in vibrations (as well as in other areas of engineering).
Proficiency in MATLAB should empower you to solve much more sophisticated
problems with relatively small “programming” effort. The rudiments
of MATLAB will be discussed in class and especially in recitation, but
you are expected to invest some time to become proficient. The program
is available on the SEAS (ENIAC) network. However, you have been
asked to purchase the Student Version of MATLAB primarily so that you will
have a complete Manual, and to give you the flexibility of using it on
any computer that you have convenient access to. Several Computer
Problems will specify the use of MATLAB, but you are encouraged to use
it in your other homework assignments, wherever applicable.
W. T. Thomson, Theory of Vibrations with Applications,Additional References:
5th Ed., Prentice Hall (1998).The Student Edition of MATLAB, Version 5, Prentice Hall (1995).
W. W. Seto, Mechanical Vibrations, Schaum’s Outline Series, McGraw-Hill (1964).(return to top)D. J. Inman, Engineering Vibration, Prentice Hall (1993).
A. Dimarogonas, Vibration for Engineers, 2nd. Ed., Prentice Hall (1996).
University
of Pennsylvania Library System
Created: August 20th, 1998
Last Update: August 21st, 1998
All rights reserved; 1998 University of Pennsylvania