Free vibration of composite laminated rectangular plates under shear deformation theory

Abstract

In this study, free vibration of anti-symmetric angle-ply, and cross-ply laminated rectangular plates under first order shear deformation theory using clamped boundary condition is analysed. Two different numerical methods called Splines approximation and Radial Basis Functions (RBFs) are considered to approximate the functions. The fundamental frequency for anti-symmetric angle-ply plates are analysed with respect to aspect ratio, length-to-thickness ratio, ply angles and number of layers with different type of material arrangements. The problem of free vibration of cross-ply laminated plates are analysed for frequency parameter with respect to length-to-thickness ratio, aspect ratio, and number of layer with different disposition of materials. For both of the problems, the equations of motion derived using Yang Nooris and Stavsky (YNS) theory and the solution is assumed in separable form to obtain a coupled differential equations in term of displacement and rotational functions. These functions are approximated using cubic Spline function for the first case and the differential equations are then approximated using RBF for the second case. Preliminary studies on anti-symmetric angle-ply laminated plates with higher order shear deformation theory under simply supported boundary condition are studied using Spline method. The free vibration of anti-symmetric angle-ply laminated plates are analysed, under third order shear deformation theory using spline approximation. The equations of motions are derived using Reddy theory with third order shear deformation theory and the solution is assumed in separable form to obtain a coupled differential equations. The displacement and rotational functions are approximated using cubic and quantic Splines. These procedures produce a set of ordinary differential equation, along with boundary condition equations and become a generalized eigenvalue problem. The resulting eigenvalue problem is solved for the frequency parameter. The frequency parameter was analysed with respect to aspect ratio, length-to-thickness ratio, ply angles and number of layers with different type of material arrangements. The aim of this research is to provide the free vibration of layered plates for anti-symmetric angleply and cross-ply laminated plate with first order shear deformation theory with clamped boundary condition and identifies the difference between two different methods applied.