To provide an introduction to the methods of analysis and design of dynamical systems: to enable students to model and to predict the performance of linear and non-linear mechanical systems.
PREREQUISITES BY TOPICS
1. Introductory mechanics.
2. Calculus through 2nd order linear differential equations with constant coefficients.
3. Eigenvalues and eigenvectors of matrices.
TOPICS
1. Modeling of lumped parameter systems.
2. Introduction to harmonic analysis.
3. Free vibration of a single-degree-of-freedom system.
4. Forced vibrations.
5. Fourier Transforms and Fast Fourier Transforms (FFT) for spectral analysis.
6. Introduction to LaPlace Transforms.
7. Convolution -- the general solution of first and second order systems subjected to arbitrary forcing functions.
8. Systems with two degrees of freedom.
9. General form of the mechanical energy for a system of particles. Equation of motion from the energy equation.
10. Derivation and application of Lagrange's equations.
11. Equations of motion of systems of several-degrees-of-freedom from the Lagrangian.
12. Dynamics of extended rigid bodies.
13. Forces in rotating systems.
COMPUTER SIMULATION LABORATORY
1. Develop Fourier series representation for a forcing function using Matlab to display the sum of several frequency components.
2. Introduction to Simulink, a software system for solving ODE subjected to a number of classical forcing functions.
3. Simulate a first-order linear electrical system using a simulation package called Simulink.
4. Simulate a second-order linear mechanical system with and without damping; and a second-order nonlinear pendulum comparing its response to the linear approximation.
ELECTRO/MECHANICAL LABORATORY PROJECTS
1. Signal generators, data acquisition and the spring-mass system.
2. Forcing of torsional pendula, using steel and plastic springs. Measurement of frequency response, using computer data acquisition and analysis system.
3. Measurement of normal modes in a vibration absorber and "shaky table" system.
4. Impulse response of 2nd order system, using instrumented hammer and computerized data acquisition.
One new experiment will be creasted to complement computer simulation 4. The results of the redesign will be posted on the Web page.
EXPECTED WORK FROM STUDENTS
* An average of a little less than a formal problem
set per week.
* Four laboratory sessions already described.
A report for each lab is required.
* One computer laboratory introduction to Matlab
with a short report.
* Three computer simulation projects associated
with linear and nonlinear dynamical systems using (SIMULINK); a report
for each project is required.
* One hour examination.
* One three-hour final examination.
COURSE GRADE
The final grade will be based on the student's written submitted response to each category of expected work, i.e., (1) homework problems, (2) computer simulations, (3) laboratory work and reports, (4) hour exam, and (5) final exam.