Environmental Disturbance Effects on Liquid Crystal Elastomer Photothermal-Oscillator Dynamics

Self-oscillations convert ambient energy into continuous periodic motion through feedback mechanisms, but their response to external periodic disturbances is not yet fully understood. Through the combination of a photothermally-responsive liquid crystal elastomer fiber and a mass block within a linear light field, we consider a liquid crystal elastomer self-oscillator. Following theoretical modeling of the light-driven self-oscillator under external periodic forcing and numerical simulations, three distinct phase-locking regimes are identified: in-phase, anti-phase, and quadrature synchronizations. Mechanisms are elucidated through time-domain, frequency-domain, and phase-space analyses. Moreover, approximate analytical expressions for the steady-state amplitude–frequency and phase–frequency responses of the self-oscillator under periodic forcing are derived using the multi-scale method. The impact of periodic forcing on the self-oscillator and its response regulation via system parameters is examined. A close correspondence exists between numerical and analytical results. This work investigates the response characteristics of a liquid crystal elastomer self-oscillator under periodic forcing, advances fundamental insights into disturbance rejection in self-oscillators, and delivers practical guidance for their robust operation in complex oscillatory settings.