Self-oscillation of a photo-actuated dual-beam system under linear optical excitation

Self-oscillating systems utilizing optically responsive liquid crystal elastomers (LCEs) are increasingly used in energy harvesting, soft robotics, and actuator applications. However, most studies expose different sections of the same LCE fiber to varying light intensity gradients, leading to local overheating and internal stress concentration, making accurate prediction and control difficult. To overcome these limitations, we propose a dual-beam system operating under a linear optical environment. A general governing equation is formulated, and its asymptotic form is derived for short characteristic times. Numerical analysis reveals a Hopf bifurcation between static and periodic modes. Using multi-scale method, the bifurcation point, oscillation amplitude, and frequency are obtained analytically, and their dependence on system parameters is systematically examined. The analytical solutions agree well with numerical results from both the governing and asymptotic equations, confirming their validity. This system overcomes the limitations of uniform-light models by enabling flexible spatial light regulation, preventing local overheating, and ensuring uniform stress and coordinated deformation. The model is compact and provides a theoretical foundation for analyzing LCE fibers under complex non-uniform or coupled stimulus fields, offering guidance for applications in soft robotics, energy harvesting, and micro-machinery.