Natural frequencies of cross-ply laminates by state space approach

Abstract

A mixed method of elastodynamics is presented for analyzing the dynamic response of laminated composite plates. The method, termed the state space approach, 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. No formal approximations are made, and the inter-layer continuity of stresses and displacements is exactly satisfied. The method is applied to obtain natural frequencies of vibration for two-layered cross-ply laminates with varying degrees of orthotropy of layers, as well as for thin to very thick plates. Comparisons are made with the results from approximate theories, and the validity of the state space approach is established by comparing with the exact elasticity solutions for plates in plane strain. The numerical results from the present theory with a limited number of terms considered in the mathematical expansion in the thickness co-ordinate are seen to be in excellent agreement with the exact results, even for very thick plates.