Commun. Nonlinear Sci. Numer. Simul. | 2021
On the size-dependent nonlinear thermo-electro-mechanical free vibration analysis of functionally graded flexoelectric nano-plate
Abstract
Abstract In the present paper, a continuous-based electromechanical model has been developed by the Kirchhoff plate s theory and the modified flexoelectric theory in order to study the size-dependent nonlinear free vibration of functionally graded flexoelectric nano-plate. Nonlinear governing coupled differential equations of motion of the nano-plate and their associated different boundary conditions for the four edges have been extracted for the first time by using Hamilton s principle and variational method. The obtained governing equations are solved by using Galerkin s and perturbation methods. The electromechanical coupling (electromechanical stress) in the internal energy function causes nonlinearity in the governing equations.The functionally graded material of the nano-plate is defined by power-law along the plate s thickness. Additionally, the plate is under the applied electric voltage and temperature rise. The natural frequencies and natural mode-shapes have been determined and shown in two cases as direct and inverse flexoelectriceffects. The results show that the size-dependency of the material properties in the presence of flexoelectric effect has significant importance in the nano-scale and with regarding to application of this type of nano-plate in oscillators, considering the flexoelectric effect. The electric potential can play an important role in adjusting and controlling the frequency.