Affiliation:
1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA
Abstract
In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)
Cited by
4 articles.
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1. PULL-DOWN INSTABILITY OF THE QUADRATIC NONLINEAR OSCILLATORS;Facta Universitatis, Series: Mechanical Engineering;2023-08-10
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4. Analytical routes of period-m motions to chaos in a parametric, quadratic nonlinear oscillator;International Journal of Dynamics and Control;2014-07-09