Chaotic vibration of mechanical systems with backlash

Abstract

Detailed numerical and experimental studies are presented on the chaotic dynamic behaviour of non-linear mechanical systems with backlash. Such systems arise in engineering structures in which components make intermittent contact due to the existence of clearances. Chaotic vibration behaviour of the system is illustrated in the time, frequency and state-space domains. Poincaré maps of the motion reveal a fractal-like structure of the attractor and the related positive Lyapunov exponents give further indication of chaotic vibration. The forcing parameter field for the existence of chaos and the influence of damping on the chaotic behaviour have been investigated. It is found that periodic as well as chaotic solutions exist under different forcing conditions. The fact that such a simple non-linear mechanical system can lead to chaotic vibration means that care must be taken in the design of mechanical control systems and that statistical stress/fatigue analysis is recommended when such systems are considered. Also, from a condition monitoring point of view, it is quite possible for a broad band response to be caused by a pure sinusoidal excitation when such non-linear mechanisms as backlash stiffness exist.