0
RESEARCH PAPERS

Analysis of Dynamic Systems With Periodically Varying Parameters Via Chebyshev Polynomials

[+] Author and Article Information
S. C. Sinha, Der-Ho Wu, V. Juneja, P. Joseph

Department of Mechanical Engineering, Auburn University, Auburn, AL 36849

J. Vib. Acoust 115(1), 96-102 (Jan 01, 1993) (7 pages) doi:10.1115/1.2930321 History: Received May 01, 1991; Online June 17, 2008

Abstract

In this paper a general method for the analysis of multidimensional second-order dynamic systems with periodically varying parameters is presented. The state vector and the periodic matrices appearing in the equations are expanded in Chebyshev polynomials over the principal period and the original differential problem is reduced to a set of linear algebraic equations. The technique is suitable for constructing either numerical or approximate analytical solutions. As an illustrative example, approximate analytical expressions for the Floquet characteristic exponents of Mathieu’s equation are obtained. Stability charts are drawn to compare the results of the proposed method with those obtained by Runge-Kutta and perturbation methods. Numerical solutions for the flap-lag motion of a three-bladed helicopter rotor are constructed in the next example. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton, and Gear algorithms. The results obtained in both the examples indicate that the suggested approach is extremely accurate and is by far the most efficient one.

Copyright © 1993 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In