Chaotic Motion of a Parametrically and Self-Excited Nonlinear Mechanical System Subjected to Harmonic Excitation

Abstract

Numerical and analytical studies are presented here which suggest that chaotic motion is possible from periodic excitation of a parametrically nonlinear mechanical system having Duffing type stiffness and van der Pol damping. Numerical integration is used to obtain phase plane portraits and Poincare maps for large-time motion. Period-doubling bifurcations and several types of limit cycles and chaotic behavior are observed. Chaotic motions are investigated using the Liapunov exponent, the invariant probability distribution, the Li-Yorke's theorem and Mel'nikov's method. Approximate analytical techniques are applied to analyze some of the limit cycles and trasitions of behavior. The results are used to predict the occurrence of chaos.