We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection beco...We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.展开更多
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2025B1515020077 and 2024A15150301-39)the National Natural Science Foundation of China(Grant No.12205138)the Shenzhen Science and Technology Innovation Committee(Grant No.JCYJ2022-0530113206015).
文摘We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.
