Instructor

Dr. Joseph C. Slater
238 Russ Engineering Center
775-5085
email: joseph dot slater at wright dot edu
http://www.cs.wright.edu/˜jslater
Helpful materials are available through the course page:
http://www.cs.wright.edu/˜jslater/Comp_Methods.shtml

Prerequisites

ME 460/660: Engineering Vibration or Equivalent

Time and Location

MW 4:10-5:50. 218 Fawcett

Homework (30%)

Homework problems will be assigned at the end of lectures. Homework problem solutions are collected every Wednesday. You will be given no less than one week to do them. If there is a test scheduled on a day homework is due, the homework will be collected the following class period. Each homework problem is worth 1 point. More difficult problems may be weighted accordingly. Your final homework score is your average total score divided by the total number of possible points. You are encouraged to work together in small groups, but keep in mind that homework is assigned in order to help you learn and keep up with the course material. Please see me if you need help with the homework. This class is a cooperative effort between you and me. You are also encouraged to do additional problems out of the text for practice on your own.

Exams (70%)

There will be one midterm and a final exam graded on a straight, scale (≥ 90 = A,≥ 80 = B,≥ 70 = C,≥ 60 = D,< 59 = F). The final exam will count for two test grades. The lowest exam grade of the three will be dropped. An 8.5 in. by 11 in. formula sheet may be used provided there are no derivations, definitions or solved problems on the sheet. Tests will be graded and returned as soon as possible. Solutions will be discussed during the lecture following the exam if time permits. All grading discrepancies must be brought up in writing no later than one week after the exam is returned. A simple note describing your contentions will do.

Important Dates

Course Contents

1. Concepts of Linear Algebra
   1. Linear Vector Spaces
   2. Linear Dependence
   3. Bases and Dimensions for a Vector Space
   4. Inner Products and Orthogonal Vectors
   5. Gramm-Schmidt Orthogonalization
   6. Properties of Matrices

2. Vibration of Discrete Systems
   1. Lagrange’s Equations
   2. Small motions about equilibrium points
   3. Energy Considerations
   4. Lyapunov Stability
   5. Self-Adjoint Systems
   6. Max-Min characteristic of eigenvalues
   7. Inclusion Principle
   8. Perturbation Methods

3. Dynamics of Continuous Systems
   1. Review of continuous system modeling
   2. Non-dimensionalization of equations of motion
   3. Concepts in Analytical Dynamics

4. Energy Methods
   1. Virtual Work
   2. Hamilton’s Principle
   3. Lagrange’s equation for continuous systems

5. The Eigenvalue problem
   1. Self-adjoint systems
   2. Orthogonality of modes
   3. Non-self-adjoint systems
   4. Repeated Eigenvalues
   5. Vibration of Rods, Shafts and Strings
   6. Bending Vibration of a helicopter blade
   7. Variational characterization of the eigenvalues
   8. Integral formulation of the eigenvalue problem

6. Discretization of Continuous Systems
   1. Rayleigh-Ritz Method
   2. Assumed Modes Method
   3. Weighted Residual Methods
      1. Galerkin’s Method
      2. Collocation Method
      3. Least Squares Method
      4. Forced Response

7. Computational Methods for the Eigensolution
   1. Gaussian Elimination
   2. Cholesky Decomposition
   3. Power Method
   4. Jacobi Method
   5. Given’s Method
   6. The Q R Method

Course Resources

Textbook

Meirovitch, L., Principles and Techniques of Vibrations, Prentice Hall, 1997.

Other Books Used in Generating Course Notes

Inman, D.J., Engineering Vibration, Prentice Hall, 1996.
Craig, Roy R., Structural Dynamics: an Introduction to Computer Methods, Wiley, 1981.
Shames, I.H. and Dym, C.L., Energy and Finite Element Methods in Structural Mechanics, McGraw-Hill, 1985.
Weaver, W., Timoshenko, S., and Young, D.H., Vibration Problems in Engineering, Wiley, 1990.
Goldstein, H., Classical Mechanics, Addison-Wesley Press, 1950.

Web Resources

Please email me from what ever account you will be using. I will add your name to the class email list so that you will receive course announcements in a timely fashion.
Use NetScape, Internet Explorer, or any other internet browser to view the class resource page at:
http://www.cs.wright.edu/˜jslater/Comp_Methods.html
On overview of MATLAB, Mathematica, and UNIX is available via my main course resource web page (up one level from the 710 page) should you choose to use any of them. Additional computer information is also available on my main course resource page.

Software

Use what you are comfortable with. I will not be able to help you with syntax, but I can help with fundamental concepts. My favorite codes for this course are (in order): Mathematica, MATLAB (and it’s clones), Fortran or C. Any of these languages that you are comfortable in will suffice. Mathematica will result in the shortest and simplest code, but it has a steep learning curve. However, it is clearly the most versatile, and I recommend learning how to use it, even if not for this course. MATLAB is the easiest language to program in. It is an interpreted language that runs slower than Fortran or C, but is ideal for working with matrices. Speed of the code is only an issue for one code, and I used MATLAB for it myself. Matlab has free clones which you can install on virtually any platform. For the purposes of this course, they are equivalent in every respect (language, speed...). They are Octave and Scilab. Octave is likely the easiest to set up, while Scilab has greater extensibility (GUI, graphics...). I use Octave even more often than MATLAB. See the links in the electronic version of this document for information on these variants.