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Analytical Solutions of a First-Order Quadratic Nonlinear System With Parametrical and Periodical Excitation

[+] Author Affiliations
Guopeng Zhou

Hubei University of Science and Technology, Xianning, China

Albert C. J. Luo

Southern Illinois University, Edwardsville, Edwardsville, IL

Naiding Zhou, Feng Liang

Huazhong University of Science and Technology, Wuhan, China

Paper No. IMECE2016-66812, pp. V04BT05A027; 7 pages
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5055-8
  • Copyright © 2016 by ASME


In this paper, a quadratic nonlinear dynamical system with two periodic excitation forces is discussed. Analytical period-1 motions of such dynamical system are obtained by using generalized harmonic balance method. Stability analysis is carried out via eigenvalues analysis. To verify approximate analytical solutions, numerical simulations are completed to compare analytic and numerical solutions of the dynamical system, the approximate precision is guaranteed with appropriate harmonic balance terms. More harmonic terms should be employed to guarantee good approximation of periodic motions if excitation frequency is small. Furthermore, infinite harmonic balance terms must be introduced for chaotic systems.

Copyright © 2016 by ASME



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