Non-linear behavior and chaotic motions of an sdof system with piecewise-non-linear stiffness

Abstract

Forced vibrations of a single-degree-of-freedom system with unsymmetric, piecewisenon-lincar restoring forces are investigated using direct numerical integration and approximate analytical methods. A simple and efficient algorithm was developed to analyse the piecewisenon-linear system by the harmonic balance method and fast Fourier transformation technique. The highly non-linear characteristics, including subharmonics, instabilities, bifurcations, Lyapunov exponents and domain of attraction, were examined. Possible occurrence of chaotic motion was investigated by means of direct numerical integration and the classical stability theory with the aid of Hill's type equation. It is found that the threshold of the onset of chaotic motion is very sensitive to any changes in system parameters, and chaotic motion will occur as the excitation amplitude exceeds certain limits.