Vibration analysis of tri-directionally coated plate via thickness-stretching and microstructure-dependent modeling

In this study, the tri-directionally-coated functionally graded plate has different levels of microstructure and is modeled more accurately using nonclassical mechanics incorporating the intrinsic characteristic lengths as well as using a spatial variation of material properties. The free vibration behavior of the tri-directionally-coated functionally graded plate is investigated using a refined quasi-3D higher-order shear deformation theory in conjunction with nonlocal strain gradient theory. Based on the generalized field of displacement, the quasi-3D higher-order shear deformation theory is employed by reducing the number of variables from six to five variables. The equations of motion are performed based on the principle of Hamilton and solved by applying the Galerkin technique to cover various boundary conditions. Besides, the microstructure-dependent parameters, that is, the nonlocal parameter and the length scale parameter, also affect significantly the frequency of the tri-directionally-coated functionally graded plates. The multi-directionally-coated plate is softened when considering the nonlocal parameter; the multi-directionally-coated plate is, however, hardened when considering the length scale parameter.