Three-dimensional free vibration analysis of functionally graded carbon nanotube-reinforced composite plates with various boundary conditions

Abstract

A unified formulation of finite prism methods (FPMs) based on Reissner's mixed variational theorem is developed for the three-dimensional (3D) free vibration analysis of functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates and laminated fiber-reinforced composite (FRC) plates, the edge conditions of which are considered such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The single-walled carbon nanotubes (CNTs) and polymer are regarded as the reinforcements and matrices, respectively, to produce the CNTRC plate. Four different distributions of CNTs varying in the thickness direction are considered (i.e. the uniformly distributed, and FG V-, rhombus-, and X-type variations), and the throughthickness distributions of effective material properties of the CNTRC plate are determined using the rule of mixtures. In the formulation, the CNTRC/FRC plate is divided into a number of finite prisms in the x À domain, in which the trigonometric functions and Lagrange polynomials are used to interpolate the y-direction and x À plane variations for the primary variables of each individual prism, respectively, and the related orders used for expansion of assorted primary variables in the thickness coordinate can be freely chosen. It is shown that the eight-and nine-node quadratic FPM solutions of frequency parameters of simply supported, CNTRC plates and laminated FRC plates are in excellent agreement with the exact 3D solutions available in the literature, and with the ones obtained using the ANSYS software for those plates with various boundary conditions.

Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach

“…The (10, 10) SWCNTs are used as the reinforcements. The material properties of SWCNTs are reported to be anisotropic, chirality and size dependent [38][39][40][41][42]. The detailed material properties of SWCNTs used for the present analysis of the FG-CNT reinforced composite plates are selected from the simulation results reported by Shen and Zhang [46] and they are tabulated in Table 1.…”

“…A two-step perturbation technique was proposed by Shen [38] to study the nonlinear bending of simply supported FG nanocomposite plates reinforced by single-walled CNTs subjected to a transverse uniform or sinusoidal load in thermal environments. A unified formulation of finite prism methods based on Reissner's mixed variational theorem was developed by Wu and Li [39] for three-dimensional analysis of FG-CNT reinforced composite plates and laminated fiber-reinforced composite plates. The thermal buckling and post-buckling behaviors of FG-CNT reinforced composite plates subjected to in-plane temperature variation were investigated by Shen and Zhang [40].…”

Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates

“…The aforementioned studies [14][15][16][17][18][19][20][21][22][23][24][25][26] have shown that the mechanical structural behaviors of FG-CNT reinforced composites can be considerably improved by the functionally graded distribution of CNTs in the matrix. Although some research on FG-CNT reinforced composite plates has been performed, the FG-CNT reinforced composite is a newly proposed composite material and more research efforts need to be made for a better understanding of this new material.…”

“…Static and dynamic analyses of FG-CNT cylindrical panels were carried out by Zhang et al [17] using the kp-Ritz method. The finite prism method was employed by Wu and Li [18] to analyze the three-dimensional free vibration of FG-CNT reinforced composite plates and laminated fiber-reinforced composite plates. Shen and Zhang [19] examined the thermal buckling behavior of FG-CNT reinforced composite plates subjected to in-plane temperature variation.…”

Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates

“…Whereas, the frequency for the FGO-CNT plate was the lowest. Wu and Li [23] used a unified formulation of Reissner's mixed variational theorem (RMVT) based finite prism methods (FPMs) to study the three-dimensional free vibration behavior of FG-CNTRC plates. Free vibration analyses of quadrilateral laminated plates were carried out by Malekzadeh and Zarei [24] using first shear deformation theory and discretization of the spatial derivatives by the differential quadrature method (DQM).…”