Self-excited vibration of a thermally expandable cantilever beam driven by a steady temperature difference

Responsive polymers can generate various self-sustained motions through the tuning of their geometric configurations, external stimuli, and boundary constraints. Research and innovation of novel self-sustained motions can broaden the scope of application for self-sustained active machines. In this paper, a novel dynamic model for the self-excited vibration of a thermally expandable cantilever beam driven by a steady temperature difference is constructed. The governing equation for the self-excited vibration of the beam is derived and solved using the modal superposition method. Numerical calculations reveal that the beam has two typical motion states, namely, the static state and the self-excited vibration state. The self-excitation mechanism is explained by the coupling between beam motion and the periodic switching of the thermally induced bending torque. The effects of each system parameter on the amplitude of the vibration in steady state are further investigated quantitatively, and the critical values for triggering the beam self-excited vibration are identified. Furthermore, the period of the self-excited vibration in steady state is almost unaffected by environmental parameters. The self-excited vibration cantilever beam holds promising potential for applications in soft robotics, energy harvesting, active motors, and self-sustained machinery.