Chaotic Behaviors of Nonlinear Vibration System with Stochastic Excitation. Probability Distribution of Local Expansion Rates.

Abstract

This paper studies chaotic behaviors of nonlinear vibration system with stochastic excitation. Previous studies dealing with mechanical chaotic vibrations have mainly focused on their deterministic properties even if the corresponding vibration system contains stochastic properties which are sometimes unavoidable in practical mechanical vibration systems. From this point, this paper mainly focuses on a random vibration arising in a stochastic nonlinear vibration system, which the authors call SCB (Stochastic Chaotic Vibration). The SCB has a negative largest Liapunov exponent while it behaves in a similar way to determinstic chaos, exhibiting expanding and folding process of chaos. This result is in good agreement with that of a practical chaotic behavior occurring in our experimental apparatus and implies that the practical chaotic behavior may not have a positive largest Liapunov exponent even though it behaves in a chaotic way. This kind of chaotic properties of the SCB and the experimental chaos can be characterized by a probability density function of local expansion rates.