Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers, micro-motors, medical equipments, and so on. Currently, numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency. However, numerical methods are burdened by intricate computations and limited precision, hindering comprehensive investigations into self-oscillating systems. In this paper, the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied, and analytical solutions for the amplitude and frequency are determined. Initially, we establish the governing equations of self-oscillation, elucidate two motion regimes, and reveal the underlying mechanism. Subsequently, we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency. The results show agreement between the multi-scale and numerical methods. This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.