Abstract:The shallow spherical shell-type bistable vibration energy harvester is first investigated in this manuscript, and the structural optimum design is established by maximizing the efficiency of the energy harvesting. First, the nonlinear stochastic differential equation is derived through the assumed mode method and the Lagrange procedure. Second, the stationary rate of expectation crossing is adopted to describe the frequency of snap through, while the deformation energy as the shell coinciding with the bottom circle to describe the harvestable energy associated with each snap through. Construct the concept of harvestable power by the product of stationary rate of expectation crossing and the referred deformation energy, and which can balance the stationary rate of expectation crossing and the referred deformation energy. Finally, the optimal non-dimensional geometric parameter and the associated non-dimensional harvestable power are derived by maximizing the harvestable power. Due to the non-dimensional property, the proposed structural optimum design keeps universality.
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