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Robust design of a nonlinear electromagnetic vibration energy harvester
Last modified: 2017-05-26
Abstract
A multiphysics model of a Vibration Energy Harvester (VEH) taking into account the effects of magnetic and geometric nonlinearities is proposed. The VEH is composed of one doubly clamped beam supporting at its middle a moving magnet and placed between two fixed magnets. The continuum problem is derived using the extended Hamilton principle, and the modal Galerkin decomposition method is used in order to obtain a reduced-order model consisting of a nonlinear Duffing equation of motion.
The resulting equation of motion is solved analytically using the method of multiple time scales and the two bifurcations points are determined. Thus, these two points are used to define the frequency and amplitude intervals of the unstable branch. Then, we examine how magnetic and mechanical design parameters impact the robustness of the device in terms of bandwidth and harvested power. More specifically, for energy harvesting applications, one of the main issues is the uncertain character of small imperfections. The introduction of these uncertainties requires more robust design. Consequently, among several design parameters, the linear and nonlinear stiffness, the equivalent mass, and the damping are considered as uncertain parameters. Stochastic effects on the performances of the proposed VEH are investigated through statistical evaluations. To do so, the Latin Hypercube Sampling method is used to perform the propagation of uncertainties. The first statistics moments of the bi-stability domain and the maximum amplitude are computed with input lognormal distribution, and also with uniform distribution for several uncertainty levels.
This method can be used as a quick analytical tool for robust design. As a first step, the expressions of the bi-stability domain and the maximum amplitude are analytically derived and secondly, the uncertainty propagation is straightforward in order to perform the robustness analysis.
The resulting equation of motion is solved analytically using the method of multiple time scales and the two bifurcations points are determined. Thus, these two points are used to define the frequency and amplitude intervals of the unstable branch. Then, we examine how magnetic and mechanical design parameters impact the robustness of the device in terms of bandwidth and harvested power. More specifically, for energy harvesting applications, one of the main issues is the uncertain character of small imperfections. The introduction of these uncertainties requires more robust design. Consequently, among several design parameters, the linear and nonlinear stiffness, the equivalent mass, and the damping are considered as uncertain parameters. Stochastic effects on the performances of the proposed VEH are investigated through statistical evaluations. To do so, the Latin Hypercube Sampling method is used to perform the propagation of uncertainties. The first statistics moments of the bi-stability domain and the maximum amplitude are computed with input lognormal distribution, and also with uniform distribution for several uncertainty levels.
This method can be used as a quick analytical tool for robust design. As a first step, the expressions of the bi-stability domain and the maximum amplitude are analytically derived and secondly, the uncertainty propagation is straightforward in order to perform the robustness analysis.