Investigation of the Effects of the Piezoelectric Patch Thickness and Tapering on the Nonlinearity of a Parabolic Converging Width Vibration Energy Harvester

Purpose It has been shown that the tapering cross-section energy harvesters' responses at high excitation amplitudes diminish due to nonlinear effects. The nonlinearities can be associated with geometry and the piezoelectric material. In this article, a nonlinear formulation of a base excited parabolic converging width piezoelectric vibration energy harvester with tip load mass considering piezoelectric and geometric nonlinearities is presented. Methods The extended Hamilton's principle and Gauss's relation are utilized to formulate the energy harvesting system's electromechanical coupled motion equations. Simultaneously, Galerkin's discretization technique is employed for the model's mass normalized mode shapes. Method of multiple scales is applied to convert the consequential nonlinear coupled motion equations into first-order differential equations. A MATLAB program is used to acquire the harvester's steady-state voltage responses, and the model verification is conducted using ANSYS simulations. Results The results show that the linear formulations are inadequate for excitation amplitudes above 2.5 g. At higher excitation levels, the eccentricity between the linear and nonlinear results is very high. At 10 g acceleration, the maximum eccentricity of 64.47% and 63.51% is observed for the model. Conclusion Increasing the taper parameter and decreasing the piezoelectric patch thickness increases the output voltage per mass of the harvester. However, the power per mass under higher excitation is not essentially increased and diminishes the scope of harvesting the maximum available abundant energy. Since the nonlinear analysis is inevitable for high excitation operations, this research can be beneficial for designing a piezoelectric vibration energy harvester for high excitation amplitude and low-frequency applications.