An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

In this article, an analytical solution to the moderately large amplitude transverse vibration of thin functionally graded micro-plates (FGMPs) is presented based on a practical approach. The size-dependent nonlinear governing equation is obtained in conjunction with the Kirchhoff’s plate and modified couple stress theories. The material properties of functionally graded (FG) micro-plates are varied according to the Reddy’s model. The employed non-classical theory contains one material length scale parameter to capture the size effects. The highly nonlinear governing equation is solved by means of homotopy analysis method to obtain accurate analytic approximations. The both of simply supported and clamped micro-plates with immovable edges are considered. Comparison of the present results with earlier studies wherever possible confirms the reliability and effectiveness of the present formulation for the design purpose. Furthermore, the effects of different parameters such as material gradient index, length scale parameter, and aspect ratio on the nonlinear frequency ratio are investigated.