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

Abstract

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 vary 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 so as to obtain accurate analytic approximations. Both of simply supported and clamped micro-plates with immovable edges are considered. The comparison made between the present results and those of earlier studies 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.