On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory

The prime aim of the present study is to predict the free vibration behavior of microplates made of functionally graded materials (FGMs). The material properties of FGM microplates are assumed to be varied across the thickness of the microplates according to the Mori–Tanaka homogenization technique. On the basis of strain gradient elasticity theory, a non-classical higher-order shear deformable plate model containing three material length scale parameters is developed which can effectively capture the size dependencies. By using Hamilton’s principle, the size-dependent governing differential equations of motion and associated boundary conditions are derived. To evaluate the natural frequencies of FGM microplates, a Navier-type closed-form solution is carried out in which the generalized displacements are stated as multiplication of undetermined functions with known trigonometric functions so as to satisfy identically the simply-supported boundary conditions at all edges. Selected numerical results are presented to reveal the influences of dimensionless length scale parameter, material property gradient index and aspect ratio on the free vibration characteristics of FGM microplates. It is found that by approaching the thickness of microplates to the value of internal material length scale parameter, the natural frequency increases considerably.