浅球壳型双稳振动能量收集器件结构优化设计

Structural optimum design of shallow spherical shell-type bistable vibration energy harvester

以浅球壳型双稳振动能量收集器件为研究对象,导出宽带随机激励下以能量收集效率最大为目标的结构优化设计方案。应用假设模态法及Lagrange方程法导出浅球壳结构非线性随机微分方程。采用稳态期望穿阈率描述结构跳变频率,并选取壳体处于底圆位置的应变能衡量每次跳变可收集能量。以稳态期望穿阈率与参考应变能乘积构造可收集功率概念,可收集功率可平衡跳变频率与每次跳变相应的可收集能量。以可收集功率最大为目标,导出最优无量纲几何参数与最优无量纲可收集功率。因其具有无量纲本质,该结构最优设计方案具有普适性。

A shallow spherical shell-type bistable vibration energy harvester was investigated,and its structural optimum design was achieved by maximizing the efficiency of the energy harvesting.A nonlinear stochastic differential equation was derived by using the assumed mode method and the Lagrange procedure.The stationary rate of expectation crossing was adopted to describe the frequency of snapping through,while the deformation energy of the shell lying at the bottom circle position to describe the harvestable energy in each snapping through.The concept of harvestable power was introduced and it is expressed as the product of stationary rate of expectation crossing and referred deformation energy, which can make a balance between these two indexes.The optimal non-dimensional geometric parameters and the associated optimal non-dimensional harvestable power were then derived by maximizing the harvestable power.Due to the non-dimensional property,the proposed structural optimum design method keeps universality.