Free vibration of symmetrically laminated plates using a higher-order theory with finite element technique

Abstract

A C⁰ finite element formulation of the higher-order theory is used to determine the natural frequencies of isotropic, orthotropic and layered anisotropic composite and sandwich plates. The material properties that are typical of high modulus fibre reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, degree of orthotropy, number of layers and lamination angle/scheme. The present theory is based on a higher-order displacement model and the three-dimensional Hooke's laws for plate material. The theory represents a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strains through the plate thickness. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The results presented should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.