Free vibration analysis of functionally graded anisotropic microplates using modified strain gradient theory

This study presents a size dependent model using the higher-order shear deformation theory (HSDT) in conjunction with modified strain gradient theory (MSGT) for free vibration analysis of functionally graded (FG) anisotropic microplates. The FG anisotropic material is made of hexagonal beryllium crystals which can be considered as a hexagonal one. To consider size effects, three material length scale parameters (MLSPs) are added into the elastic constants of the anisotropic material. Based on the principle of virtual work, discretized governing equations of the FG hexagonal microplates are obtained. Subsequently, the natural frequency of the FG anisotropic microplates is determined by using isogeometric analysis (IGA). Numerical results show that the natural frequency of the FG anisotropic microplates is influenced by the geometry, boundary condition, length-to-thickness ratio, exponential factor and material length scale parameter. The results of classical HSDT model can be restored from the present model when three MLSPs equal to zero. Moreover, the differences of the natural frequency predicted by MSGT and classical HSDT can grow up more than 4.5 times.