Applied Mathematics and Mechanics >
Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field
Received date: 2023-10-12
Online published: 2024-01-27
Supported by
the National Natural Science Foundation of China(12172001);the Anhui Provincial Natural Science Foundation of China(2208085Y01);the University Natural Science Research Project of Anhui Province of China(2022AH020029);the Housing and Urban-Rural Development Science and Technology Project of Anhui Province of China(2023-YF129);Project supported by the National Natural Science Foundation of China (No. 12172001), the Anhui Provincial Natural Science Foundation of China (No. 2208085Y01), the University Natural Science Research Project of Anhui Province of China (No. 2022AH020029), and the Housing and Urban-Rural Development Science and Technology Project of Anhui Province of China (No. 2023-YF129)
Copyright
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.
Haiyang WU, Jiangfeng LOU, Biao ZHANG, Yuntong DAI, Kai LI . Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field[J]. Applied Mathematics and Mechanics, 2024 , 45(2) : 337 -354 . DOI: 10.1007/s10483-024-3080-5
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