ME 710 : Computational Methods in Structural Dynamics

Dr. Ravi C. Penmetsa
Room: 227 Russ Engineering Center
Phone: 775-5089

E-mail:     
pravi@cs.wright.edu

Web Page:
http://www.wright.edu/~ravi.penmetsa

Office Hours:
Distributed in Class

Location:
Check ROX

Prerequisites:
ME 460/660: Engineering Vibration or Equivalent OR prior approval by Instructor

Course Objective

Identify the difference between a discrete and continuous systems.

Take any physical system and model it as a discrete or continuous system. And justify why each of those models is valid.

Analyze the models developed by estimating the Equation of Motion.
Analyze the stability of discrete and continuous systems.

Course Resources

Textbook

 

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

Optional Readings
  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.

Course Structure

Homework

 

Homework problems will be assigned at the end of each lecture to test students understanding of the material covered. Homework solutions will be collected a week from the day the questions were distributed. Each homework is worth 30 points. Your final homework score is your average total score of all the homework’s. Please see me should you experience any trouble with your 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
  There will be one mid-term and a final exam graded on a straight, scale (>90 = A, >80 = B, >70 = C, >60 = D, <59 = F). 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.

Attendance and Class Participation

Attending all classes is essential. If for some unavoidable reason you must miss a class, please let your instructor know in advance in writing so that your absence will not be unexplained. Students are expected to complete their assignments on time and come to class prepared to discuss the material. This material is not simple, be sure to raise questions when you do not understand a concept. It is very important not to fall behind in this course.

Grading

Homework

25%

Midterm Exam

35%

Final Exam

35%

Attendance and Class Participation

5%

NOTE: NO MAKE UP EXAMS WILL BE GIVEN. THE INSTRUCTOR RESERVES THE RIGHT TO ADJUST THE GRADING SCALE IF HE BELIEVES THAT THE EXAM OR ASSIGNMENTS HAVE BEEN PARTICULARLY DIFFICULT OR EASY.

Course Contents

Concepts in Analytical Dynamics

Newton’s Second Law of Motion
Hamilton's Principle
Lagrange’s Equations of Motion
Eigenvalue Problem
Self Adjoint Systems

Multi-Degree of Freedom Systems

Equations of Motion
Stability of Equilibrium Points
Linearization About Equilibrium Points

Qualitative Behavior of the Eigensolution

Inclusion Principle
Perturbation of Eigenvalue Problem

Computational Methods for the Eigensolution

Gaussian Elimination
Cholesky Decomposition
Power Method
Jacobi Method
Given¹s Method
The Q R Method

Dynamics of Continuous Systems

Vibration of Rods, Shafts and Strings
Bending Vibration of Bars

Discretization of Continuous Systems

Rayleigh-Ritz Method

Weighted Residual Method

1 Galerkin¹s Method
2 Collocation Method
3 Least Squares Method

Important Dates

Distributed in Class  
   
 

Academic Dishonesty

The university policy on academic dishonesty can be found in the student handbook. Make sure you read it, particularly the sections regarding suggestions for student prevention of academic dishonesty. Academic dishonesty will be prosecuted in accordance with university guidelines.


© Dr. Ravi Penmetsa 2004. All rights reserved