Three-dimensional elasticity solution for vibrational analysis of thick continuously graded sandwich plates with different boundary conditions using a two-parameter micromechanical model for agglomeration

An equivalent continuum model based on the Eshelby-Mori-Tanaka approach was employed to estimate the effective constitutive law for an elastic isotropic medium (i.e., the matrix) with oriented straight carbon nanotubes (CNTs). The two-dimensional generalized differential quadrature method was an efficient and accurate numerical tool for discretizing equations of motion and for implementing various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, and all possible combinations of free, simply supported, and clamped boundary conditions were applied to the other two edges. The CNTs volume fraction varied based on the thickness of the functionally graded carbon nanotube-reinforced plate and the generalized power-law distribution of four parameters. The effects of geometrical and material parameters and boundary conditions on the frequency parameters of the laminated functionally graded nanocomposite plates were investigated, and the results revealed that the natural frequencies of the structure were significantly affected by the influence of CNT agglomeration.