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QUASI-PERIODIC RESPONSE AND STABILITY ANALYSIS FOR NON-LINEAR SYSTEMS: A GENERAL APPROACH

✍ Scribed by Y.-B. Kim

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 512 KB
Volume: 192
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1996.0220

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✦ Synopsis

A modified FPA (Fixed Point Algorithm) is developed to analyze quasi-periodic responses of strongly non-linear dynamical systems with multi-input frequencies. An accurate and explicit form of the Jacobian matrix is used in the iteration process by selecting discrete integral points in the Poincare´map. The monodromy matrix, obtained from discrete integral points on the second order Poincare´domain, can accurately provide the stability condition as well as the bifurcation characteristics for the calculated quasi-periodic solution. Two examples are shown to illustrate the detailed application of the method. The proposed method can be utilized for obtaining the stable quasi-periodic responses as well as for analyzing the bifurcation characteristics of unstable solutions of general non-linear dynamical systems with multiple input excitation frequencies.

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