Thermomechanical Dynamic Instability Analysis of Pseudo-elastic MEMS Vibration Energy Harvesters under Non-Gaussian Bounded Random Excitations

Thermomechanical instability in pseudo-elastic cantilever energy harvesters driven by non-Gaussian stochastic excitations was investigated in this article. It was shown that the interplay of nonlinear restoring forces and SMA hysteresis yields rich dynamic behavior that markedly affects stable zones and energy output. Although nonlinearities can enhance harvesting efficiency, they may also induce chaos under certain thermomechanical and stochastic conditions. Despite extensive numerical studies, a fully analytical, non-dimensional framework for combined thermomechanical and stochastic forcing in SMA-based cantilevers is lacking. Here, using the modified Melnikov's function for stochastic systems, we develop such a framework and derive stability boundaries as functions of ambient temperature variation and noise bandwidth. Our results illuminate how operating near edited parameter regimes can maximize energy conversion while maintaining robust performance, and provide design guidelines for MEMS energy harvesters subject to realistic, broadband excitations. The analytical predictions are corroborated with some Poincaré mapping of selected results.