Nonlinear analysis of functionally graded piezoelectric energy harvesters

This study deals with nonlinear vibrational analysis of functionally graded piezoelectric energy harvesters (FGPEH) carrying concentrated mass at free end, while taking into account the geometrical nonlinear terms as well as electromechanical couplings. Hamilton's principle and Rayleigh's beam theory are utilized to obtain the coupled electromechanical governing equations. The first mode shape of the system is derived analytically which is also validated by comparing it with numerical findings of a three-dimensional finite element simulation performed in COMSOL Multiphysics commercial software. The Galerkin projection method is employed along with a single mode approximation to derive the nonlinear coupled electromechanical governing equations which are then solved analytically using the method of multiple time scales perturbation technique for both cases of free and forced vibrations. Time domain responses of free vibration are compared with those of numerical simulations carried out in MATLAB and excellent agreement is observed. Moreover, the nonlinear frequency responses of the forced vibration are obtained for the case of near resonance excitation. A parametric study is also accomplished to reveal the effects of power low index of the FG material as well as the scaled amplitude of the input displacements of the base on the shape of the frequency response.