Modeling of self-oscillating flexible circuits based on liquid crystal elastomers

•A conceptual self-oscillating liquid crystal elastomer-based flexible circuit was presented.•The system has two typical motion patterns: static and self-oscillation pattern.•The amplitude and frequency of self-oscillation can be designed by several parameters.•An automatic control device and a disturbance monitoring device were conceptualized. Deformable and movable flexible circuits are characterized by simple construction, precise control, flexible and versatile morphology, and various functional forms, which can be used to build dynamic circuit systems, achieve the integration of drivers and controllers, and automated control of circuits, etc. Limited to conventional materials, challenges remain in designing novel self-oscillating flexible circuit. In this paper, a concept for a self-oscillating flexible circuit based on electrothermally responsive liquid crystal elastomers (LCEs) is presented, which is capable of generating periodic continuous oscillation under steady applied voltage. The governing equation of the self-oscillating LCE-based flexible circuit is formulated, and numerically calculated by fourth-order Runge-Kutta method with Matlab software. The numerical calculations reveal that the self-oscillating flexible circuit involves two motion patterns, i.e., static pattern and self-oscillation pattern. The self-oscillation arises from the coupling between the electrothermally driven deformation of the LCE film and its motion, and the electrothermal input compensates for the damping dissipation. Moreover, it is found that system parameters affect the self-oscillation of flexible circuit and that there are critical values of these parameters that trigger self-oscillation. Based on the self-oscillating flexible circuit, we conceptualized an automatic control device and a disturbance monitoring device, realizing automatic control of electrical appliances without human intervention and automatic monitoring of external disturbances. The proposed self-oscillating LCE-based flexible circuit features convenient operation, simple construction, flexibility, lightweight, and noiseless operation, rendering it suitable for constructing dynamic circuit systems, achieving actuator-controller integration, and facilitating circuit automation applications. Conceptual self-oscillating flexible circuits utilizing electrothermally responsive liquid crystal elastomers under steady applied voltage have two motion patterns: static and self-oscillation, which can be adj