Analytical and numerical simulations of energy harvesting using MEMS devices operating in nonlinear regime

While macro-scale piezoelectric generators require base excitations with moderately large amplitudes to transit from the linear regime of vibration to the nonlinear one, for a MEMS harvester due to its small dimensions, this transition can occur at oscillatory base motions even smaller than a few microns, which necessitates the nonlinear analysis of MEMS harvesting devices in most environments. In this paper the coupled electromechanical behavior of a typical MEMS-based piezoelectric harvester in the nonlinear regime is investigated. Lagrange’s equations are used in accordance to the assumed mode method to extract the coupled nonlinear equations of motion governing the lateral deflection and output voltage. An analytical solution to the derived equations is performed employing the perturbation method of multiple scales providing the nonlinear frequency responses of the output power. Results indicate that although the effect of nonlinear inertia increases due to utilizing large tip masses in these harvesters, nonlinear curvature is still the dominant effect leading to hardening behavior of the response. The comparison of the responses of the nonlinear and linear devices shows a considerable enhancement of the frequency bandwidth in the nonlinear regime. Also a nonlinear coupled electromechanical FE simulation of the harvester is conducted using the ABAQUS software where a very good agreement is observed between the results of this simulation with both analytical and numerical solutions of the governing equations.