Analyse de la vibration libre des plaques composites sur fondation élastique.

Abstract

A free vibration analysis of laminated composite plates on elastic foundation is examined by a refined hyperbolic shear deformation theory in this paper. This refined plate theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a hyperbolic function across the plate thickness, so account for parabolic distributions of transverse shear stresses and satisfy zero shear stress conditions at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modelled as two parameter Pasternak type foundation and Winkler type if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on elastic foundation is obtained through Hamilton’s principle. The numerical results obtained through the present analysis for free vibration of cross-ply laminated plates on elastic foundation are presented, and compared with the ones available in the literature. It can be concluded that the proposed theory is not only accurate but also efficient in predicting the natural frequencies of laminated composite plates.