Free vibration analysis of multilayer functionally graded polymer nanocomposite plates reinforced with nonlinearly distributed carbon-based nanofillers using a layer-wise formulation model

Abstract

This paper investigates the influence of linear and nonlinear distribution of nanofillers on the vibrational behavior of nanocomposite plates using a layer-wise formulation model. Two separate kinds of nanocomposite plates are considered in this study; multilayer functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates, and multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates. The carbon-based nanofillers are assumed to be either uniformly dispersed or functionally graded across the plate thickness direction. Those distributions can be in linear or non-linear form. The governing equation is obtained employing the first order shear deformation theory (FSDT). The rule of mixture is used to calculate the effective elastic modulus for the CNTRC plate, while for the GPLRC plate, the modified Halpin-Tsai micromechanics model is employed, however, the mass density and Poisson's ratio are determined by using the rule of mixture for both types of nanocomposite plates. A validation study is carried out in order to take an idea on the degree of precision of our results comparatively with those available in the literature, thereafter, a parametric study was performed focusing on the (i) effect of total number of layers for (ii) linearity and non-linearity cases of nanofillers distribution, (iii) nanofillers weight fraction and distribution types, (iv) plate length/width and width/thickness ratios, and (v) boundary conditions on the natural frequencies of the FG-CNT and FG-GPL reinforced composite plates. The results indicate that changing the nanofillers distribution patterns from a uniform to non-uniform way using the proposed layer-wise formulation model can remarkably increase or decrease the effective stiffness of the plate structures.