Bifurcation analysis in liquid crystal elastomer spring self-oscillators under linear light fields

Self-oscillating systems based on active materials have been extensively constructed, which are emerging as attractive candidates for promising applications including energy harvesting, autonomous robotics, actuators, and so on. Currently, the properties of self-oscillations, such as amplitude, frequency, and bifurcation points, are generally obtained by numerical methods, which limits their applications. In this paper, we construct a light-fueled spring self-oscillator system, perform bifurcation analysis, and derive analytical solutions for the amplitude and frequency of the self-oscillations. The proposed spring self-oscillator system is composed of a liquid crystal elastomer (LCE) fiber and a mass under a linear light field. Based on the well-established dynamic LCE model, the governing equations of the system are derived and linearized. Through numerical calculation, two motion regimes of the system are found and the mechanism of self-oscillation is revealed. Moreover, the multi-scale method is employed for solving the governing equations and deriving the analytical solutions for frequency, amplitude, and bifurcation points. Following this, the study examines how system parameters impact frequency, amplitude, and bifurcation points, demonstrating agreement between the analytical results and numerical results. The straightforward analysis of the self-oscillating systems through the well-known multi-scale method greatly aids in the design and control of such systems. Meanwhile, the results furnish new insights into understanding of self-oscillating phenomenon and provide a broader range of design concepts applicable to soft robotics, sensors, and energy harvesters.