Vibration of elastically restrained cross-ply laminated plates with variable thickness

Abstract

The natural frequencies of symmetrically laminated plates of variable thickness are analyzed using the finite strip transition matrix technique. In this paper, the natural frequencies of such plates are determined for edges with being elastically restrained against both rotation and transition or both. A successive conjunction of the classical finite strip method and the transition matrix method is applied to develop a new modification of the finite strip method to reduce the complexity of the problem. The displacement function is expressed as the product of a basic trigonometric series function in the longitudinal direction and an unknown function that has to be determined in the other direction. Using the new transition matrix, after necessary simplification and the satisfaction of the boundary conditions, yields a set of simultaneous equations that leads to the characteristic matrix of vibration. The mode shapes and the frequency parameters for different combinations of elastic or translational restraint coefficients have been presented and compared with those available from other methods in the literature. Also, the effect of the tapered ratio and the aspect ratio on the natural frequencies and the mode shapes of the plates are presented. The good agreement with other methods demonstrates the validity and the reliability of the proposed method.