Abstract
Self-oscillating coupled machines are capable of absorbing energy from the external environment to maintain their own motion and have the advantages of autonomy and portability, which also contribute to the exploration of the field of synchronization and clustering. Based on a thermally responsive liquid crystal elastomer (LCE) spring self-oscillator in a linear temperature field, this paper constructs a coupling and synchronization model of two self-oscillators connected by springs. Based on the existing dynamic LCE model, this paper theoretically reveals the self-oscillation mechanism and synchronization mechanism of two self-oscillators. The results show that adjusting the initial conditions and system parameters causes the coupled system to exhibit two synchronization modes: in-phase mode and anti-phase mode. The work conducted by the driving force compensates for the damping dissipation of the system, thus maintaining self-oscillation. The phase diagrams of different system parameters are drawn to illuminate the self-oscillation and synchronization mechanism. For weak interaction, changing the initial conditions may obtain the modes of in-phase and anti-phase. Under conditions of strong interactions, the system consistently exhibits an in-phase mode. Furthermore, an investigation is conducted on the influence of system parameters, such as the LCE elastic coefficient and spring elastic coefficient, on the amplitudes and frequencies of the two synchronization modes. This study aims to enhance the understanding of self-oscillator synchronization and its potential applications in areas such as energy harvesting, power generation, detection, soft robotics, medical devices and micro/nanodevices.