Performance analysis of the functionally graded flexoelectric-piezoelectric energy harvesting

In the present paper, the output performances of the functionally graded flexoelectric-piezoelectric (FGFP) energy harvesting subjected to an external harmonic excitation, considering the effect of piezoelectric polarization direction, are addressed. Based on the Euler-Bernoulli beam model and generalized Hamiltonian principle, the dynamic governing equations and the corresponding boundary conditions of the functionally graded flexoelectric-piezoelectric energy harvesting are obtained. The natural frequency equation and the closed-form analytical expressions of electromechanical responses are further deduced. The numerical results show that the output performance of the functionally graded flexoelectric-piezoelectric energy harvesting is dependent on the piezoelectric polarization direction, gradient index and structure size. At the nanoscale, the flexoelectric effect dominates the output performances; however, at the microscale, the gradient piezoelectric effect dominates the output performances. At transition scales, from nano to micro, the output performances are very small sometimes, where, in some case, the gradient piezoelectric effect and flexoelectric effect cancel each other. The present study reveals the importance of the piezoelectric polarization direction and gradient index on the output performance of the functionally graded flexoelectric-piezoelectric energy harvesting from nano to micro scales.