Analysis of Chaotic Characteristics of the Strong Nonlinear Vibration Isolation System Based on Harmonic Balance Method

Abstract:

The key of studying the nonlinear system of the stationary period solutions by the HBM is solving a group of higher order multi-degree-of-freedom nonlinear equations. Aiming at this difficulty, this paper can easily get a higher harmonic balance truncation order expression of solution using a powerful symbolic computation software, and avoid the tedious derivation process. And the main subharmonic response range was accurately obtained by the EACM for solving the nonlinear equations. Meanwhile, the chaotic region was estimated through subharmonic cascade regions combined with the bifurcation of the Feigenbaum rule by solving the system. And, numerical results calculated by the Runge-Kutta method were given to verify the results of the period doubling bifurcations and chaotic region obtained by this method. It has been shown that they are in good agreement.

• Periodical: Applied Mechanics and Materials (Volumes 635-637)
• Pages: 117-122
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.635-637.117
• Online since: September 2014
• Authors: Wei Min Mao, Hui Zhang*, Jing Jun Lou
• Keywords: Chaos, Equal Arc-Length Continuation Method (EACM), Harmonic Balance Method (HBM), Subharmonic Bifurcation

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