Vibrational study on multilayer sandwich plates: porous FGM core, nanocomposite and piezoelectric face sheets

Abstract

A quasi-3D sinusoidal shear deformation theory and an analytical solution are presented for free vibration analysis of a 5- layer sandwich plate. The core of the sandwich plate is composed of a functionally graded porous (FGP) material that is distributed in two different types of nonlinear functions. The porous core is surrounded by two randomly oriented straight single walled CNT reinforced layers and two piezoelectric face sheets. Eight various couples of distribution of CNTs are considered for interior layers of the sandwich plate. Symmetric distributions include uniform distribution and FG-XX, FG-OO, and FG-VA and asymmetric distributions are FG-XO, FG-UO, FG-UX, and FG-AV. Effective elastic moduli of the nanocomposite layers are calculated by Mori-Tanaka approach; the set of the governing equations are derived using Hamilton’s principle and are solved for the simply supported boundary conditions using Navier’s method. Accuracy of the presented solution is confirmed and effects of different parameters on the natural frequencies of the plate are studied including aspect ratio, porosity parameter, porosity distribution pattern, volume fraction and distribution pattern of CNTs and Winkler and shear coefficients of the foundation.