Frequency analysis of symmetrically laminated plates with free edges

This paper is concerned with the estimation of natural frequencies of undamaged symmetrically laminated plates (rectangular, circular, annular and elliptical) having completely free edges. The Rayleigh-Ritz energy approach is employed here to obtain the approximate natural frequencies and the associated mode shapes. The plates are considered to be thin and to undergo small deflections satisfying Kirchhoff's hypothesis. A complete power series is used as admissible functions for in-plane and out-of-plane displacements. In the numerical examples, the accuracy of the present results is compared with the other analytical results available in the literature. The effects of the shape and size of the plate, number of plies and the fiber orientation on the natural frequencies (flexural mode) of symmetrically laminated plates are documented. The mode shape corresponding to each frequency has been identified in this paper.