Random Response Analysis And Structural Optimum Design Of Bistable Vibration Energy Harvesting Devices

Bistable vibration energy harvesting devices are especially suitable to scavenge the broadband energy in real environment due to its high energy converting efficiency and the robustness to the changing of load and structural parameters. This thesis firstly develops a semi-analytical procedure to evaluate the random response of bistable vibration energy harvesting devices under Gaussian white noise excitation. Then, based on the above results, the structural optimum design for the shallow spherical shell-type and the cylindrical shell-type bistable harvesting devices are investigated, respectively, and universal design curves are established.In the aspect of random response prediction, a two-step approximation procedure is developed to deal with the coupled nonlinear stochastic differential equations. The influence of the harvesting circuit on the mechanical subsystem comes down to the modified conservative mechanism and modified dissipative mechanism. The modified mechanical system associated with the original coupled system is then derived explicitly by introducing the generalized harmonic transformation. Suppose a nonlinear stochastic system family, each element of which possesses the analytically stationary probability density. Then, the equivalent nonlinear system of the modified mechanical system is selected from the nonlinear stochastic system family, and determined by minimizing the mean square difference between them. The statistic quantities of the original coupled system are approximated by those of the equivalent nonlinear system.In the aspect of structure optimization design, two kinds of typical bistable energy harvesting devices, i.e., the shallow spherical shell-type and the cylindrical shell-type, are investigated respectively. The nonlinear stochastic differential equations are firstly derived through the assumed mode method and the Lagrange procedure. Secondly, the stationary rates of expectation crossing are adopted to describe the frequency of snap through, while the deformation energy as the shallow spherical shell coinciding with the bottom circle and the cylindrical shell getting to the plane which decided by the two simply support’s straight edges are selected as referred deformation energy and to describe the harvestable energy associated with each snap-through behavior. Construct the concept of harvestable power by the product of stationary rate of expectation crossing and the referred deformation energy, and then, the optimally non-dimensional geometric parameter and the associated optimally harvestable power are derived by maximizing the harvestable power.