Vibration of Cross-Ply Laminated Composite Plates

Abstract

Natural frequencies of cross-ply laminated composite plates are analyzed in this chapter taking into account the effects of higher-order deformations and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two dimensional higher-order theory for rectangular laminates is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported laminated plate. Convergence properties of the lowest natural frequency are examined in detail. Numerical results are compared with those of the published existing theories and finite element method solutions. The present global higher-order theories can provide accurate results for natural frequencies of general cross-ply laminated composite plates. The chapter claims that the present approximate higher-order theories is (6M - 1), which is not dependent on the number of layers in any multilayered plates. The present theory has the advantage of predicting natural frequencies of cross-ply multilayered composite plate without increasing the unknowns involved, as the number of layers increases. The distribution of modal stresses in the thickness direction has also been obtained accurately in the ply level.