Global dynamics of the dry friction oscillator with shape memory alloy

Abstract

As a new functional material, shape memory alloy (SMA) can simplify the traditional mechanical structure and design a compact vibration control system. Meanwhile, friction is common in vibration control system, the study of friction is beneficial to the global dynamical analysis. In this paper, the global structure of the dry friction oscillator with SMA is studied by the modified composite cell coordinate system (CCCS) method. By analyzing the influence of excitation amplitude, friction and temperature on global bifurcation, the evolution process of the crisis phenomena with the variation of parameters is illustrated in detail. There exist three kinds of crises including merging crisis, boundary crisis and interior crisis. Moreover, when multiple attractors coexist in the state space, a series of basin boundary metamorphoses, such as smooth-fractal, fractal-Wada and Wada-Wada are also discovered as the temperature and the friction varies. The results show that the modified CCCS method is a powerful tool to reveal the mechanism of crises in the non-smooth system and also demonstrate that the motion of the system can be regulated with the variation of parameters, so as to control the system vibration.