Analytical modeling for free vibration of functionally graded piezoelectric energy harvester with geometric nonlinearities

Due to high efficiency of piezoelectric transducers in conversion of wasted mechanical energy to useful electrical energy they have received much interest during the last decade. In order to reduce the stress concentration, removing the brittleness of the piezoceramics and tuning the resonance frequency, they can be fabricated as functionally graded materials. This study deals with nonlinear free vibration analysis of functionally graded piezoelectric energy harvester (FGPEH) carrying concentrated mass at the free end. The theoretical formulation is based on the Euler-Bernoulli beam assumption with geometric nonlinearity and Rayleigh’s beam theory for considering the effect of rotary inertia. The analytical expression for the responses of the model is presented using the multiple scale perturbation method. To assess the accuracy of the proposed method, a three-dimensional finite element simulation is performed using COMSOL Multiphysics commercial software. Adopting a certain value of the graded index may be useful in design of FGPEH.