Free vibration analysis of functionally graded rectangular Nano-plates with considering surface effect based on nonlocal elasticity theory

< p >The aim of this paper is to study the free vibration of functionally graded rectangular nano-plates with considering surface effect. The Nonlocal elasticity theory and surface elasticity theory based on the modified shear deformation theories has been used to obtain the natural frequency of the nano-plate. In modified shear deformation theories, various functions such as exponential function, hyperbolic function and etc. are used to include the effect of transverse shear deformation and rotary inertia. Nonlocal elasticity theory and surface elasticity theory are employed to considering effect of nonlocal parameter and surface effect on the natural frequency of functionally graded rectangular nano-plate respectively. The properties of materials vary continuously through the thickness according to Mori-Tanaka scheme. The governing differential equations of vibration of functionally graded nano-plate are derived by using the Hamilton’s principle and this equations solved by using the Galerkin method to obtain the natural frequencies. Finally, the effect of various parameters such as surface parameters, nonlocal parameters, aspect ratio (a/b), length to thickness ratio (a/h) and Power Law indexes on the natural frequency of nano-plate are presented.