Global dynamics of the dry friction oscillator with shape memory alloy
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O R I G I NA L
Xiaole Yue · Yilin Xiang · Yong Xu · Ying Zhang
Global dynamics of the dry friction oscillator with shape memory alloy
Received: 17 January 2020 / Accepted: 22 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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, fractalWada 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. Keywords Global dynamics · Dry friction · Shape memory alloy · Modified composite cell coordinate system method
1 Introduction In practical engineering, there are a lot of non-smooth factors, such as gap, impact and dry friction, which have strong nonlinearity and singularity. With the development of nonlinear dynamics, the scholars began to combine the non-smooth factors with the idea of dynamic system and found many new phenomena [1,4]. As a typical non-smooth factor, the dry friction leads to serious vibration and reduces the operating efficiency of mechanic systems. Therefore, it has become an important research direction to study the stability, bifurcation and chaos of the dry friction system. Popp et al. [25] discovered different stick-slip motion and paths to chaotic motions in dry friction oscillators with external excitation. Licskó G et al. [20] investigated the crossing-sliding type that causes symmetry breaking in a dry friction oscillator. Webber et al. [34] studied the microscopic loss of X. Yue · Y. Xiang · Y. Xu · Y. Zhang (B) Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China E-mail: [email protected] X. Yue E-mail: [email protected] Y. Xiang E-mail: [email protected] Y. Xu E-mail: [email protected]
X. Yue et al.
determinacy in dry friction oscillators. Jin et al. [18] established an approximate analytical method to evaluate the dynamic response of Duffing system including dry friction. As an intelligent material, SMA has many unique mechanical properties, such as shape memory effect a
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