Jiang Bai

Publication Date

1996

Document Type

Dissertation/Thesis

First Advisor

Fallahi, Behrooz

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering

LCSH

Chebyshev polynomials; Rotational motion (Rigid dynamics)--Mathematics

Abstract

A numerical scheme based on Chebyshev Polynomials for the determination of the response of dynamic systems is presented. The approach is based on the expansion of the state vector and its coefficient matrix in terms of Chebyshev Polynomials. This expansion reduces the original differential equations to a set of linear algebraic equations where the unknowns are the coefficient of Chebyshev Polynomials. Three applications are presented. The first application is a one degree of freedom linear dynamic system. The second application is a two degree of freedom linear dynamic system. The third application is a rotating Timoshenko beam. The numerical results are compared with that o f analytical method and Newmark method. The CPU time is compared with that of Runge Kutta?s method and Newmark method. A numerical study is conducted to investigate the effect of order of Chebyshev Polynomials used and the number of subintervals on CPU time and accuracy of the method presented in this work. It is concluded that this scheme not only provide accurate solution but it is also computationally very efficient.

Comments

Includes bibliographical references (pages [45]-47)

Extent

vii, 47 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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