An efficient solution to the free vibration of thick angle-ply laminae

Abstract

A mixed method of elastodynamics, termed the state space approach, is presented for analyzing the dynamic response of composite plates. The method is based on the principle of reducing the governing three-dimensional equations to a set of two-dimensional equations while keeping the field equations in their exact form. Natural frequencies of vibration for thick orthotropic laminae with varying angles of inclination of the orthotropic axes are presented for two distinctly different materials and for large values of thickness. Comparisons with the exact solution of the three-dimensional equations of elasticity establish the effectiveness of the present approach for the class of problems considered. The numerical results from the present theory with a limited number of terms considered in the mathematical expansion in the thickness coordinate arc seen to be in excellent agreement with the exact results even for very thick plates.