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 Kirchhoʹs plate and modied couple stress theories. The material properties of Functionally Graded (FG) micro-plates vary according to the Reddyʹs model. The employed non-classical theory contains one material length-scale parameter to capture the size eects. 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 conrms the reliability and eectiveness of the present formulation for the design purpose. Furthermore, the eects of dierent parameters, such as material gradient index, length-scale parameter, and aspect ratio, on the nonlinear frequency ratio are investigated.