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

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