In this study, the instability borders of a two-dimensional simply supported laminated plate made from a magnetic shape memory alloy (MSMA), functioning as a vibration harvester under non-Gaussian in-plane bounded noises, were obtained using an analytical approach. The nonlinear governing equation of vibration was derived by considering large deformations, randomness, magnetostriction effects, super elasticity, and broadband excitation. By introducing dimensionless parameters, we aimed to achieve general, case-independent results. The modified version of Melnikov’s function for random systems was first derived and then used to obtain fully analytic results for the instability zones of the response. These boundaries were plotted based on noise properties (amplitude, frequency, and bandwidth) along with variations in magnetic field intensity (MFI) and plate aspect ratio. We believe that the findings and results of this article can help identify suitable operating zones for a broad spectrum of these types of vibration energy harvesters.
Asnafi et al. (Tue,) studied this question.