Nonlinear Vibration Analysis of Functionally Graded Rectangular Plates under Some Given Boundary Conditions by Yongyue Han Thesis Supervisor: Prof. Guo-Kang Er Department of Civil and Environment Engineering In this thesis, nonlinear vibration analysis of functionally graded rectangular plates under some given boundary conditions is studied. Nonlinear vibration analysis is presented for a simply supported, functionally graded rectangular plate subjected to a transverse uniform load. Material properties are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded plate are based on Reddy’s higher-order shear deformation plate theory. Two cases of the in-plane boundary conditions are considered. Galerkin technique is employed to determine the load-deflection. The numerical illustrations concern nonlinear displacement response and frequency curves of functional graded rectangular plates with two constituent materials. The character of in-plane boundary conditions, plate aspect ratio and volume fraction distributions are studied.