In this thesis, bending and free vibration of rectangular micro/nanoplates resting on elastic foundation is studied based on the three-dimensional elasticity and size-dependent theories of modified couple stress and Eringen's nonlocal elasticity. The plate is assumed to be made of functionally graded material (FGM). At first, it will be shown that the nonlocal theory of Eringen is not generally suitable for analysis of FGMs at micro/nano scale and should be modified. In modified version, an imaginary nonlocal strain tensor is introduced and used to directly obtain the nonlocal stress tensor. Then, governing equations and boundary conditions including dynamic phrases and transverse loads are extracted for one-layered FGM micro/nanoplates and homogeneous micro/nanoplates coated by FGM layer based on the three-dimensional elasticity and theories of modified couple stress, Eringen's nonlocal elasticity and modified nonlocal elasticity. The obtained equations are solved analytically for simply-supported boundary conditions. To obtain the analytical solution, material properties are assumed to vary exponentially through the plate thickness. The equations of motion are solved using two proposed displacement fields for the in-plane and out-of-plane vibration modes that satisfy simply supported boundary conditions. By inserting the displacement fields in the 3-D elasto-dynamic equations, some independent ordinary differential equations are obtained and solved analytically. In the following, generalized differential quadrature method is used to solve bending and free vibration of one-layered FGM micro/nanoplates and homogeneous micro/nanoplates coated by FGM layer with different boundary conditions. Then, comprehensive results are presented that can be used as a benchmark to validate future studies because of their high accuracy. Based on numerical result, it is observed that including the nonlocal effects leads to rigidity reduction of plates, whereas including the couple stress effects yields an increase in the rigidity of plates. Also based on numerical results, the third-order plate theory in the framework of modified couple stress theory is not suitable to analyze mechanical behavior of plates. Key Words: FGM micro/nanoplates, Bending, Free vibration, Three-dimensional elasticity theory, Exact closed-form solution, Generalized differential quadrature method.
