Three-dimensional vibration of laminated composite plates and cylindrical panels with arbitrarily located lateral surfaces point supports

On the basis of fully three-dimensional elasticity considerations, this paper presents a free vibration analysis of simply supported, cross-ply laminated plates and cylindrical panels that are subjected to an arbitrary number of lateral surfaces point supports. The analysis is based on a recursive approach suitable for the vibration analysis of corresponding unconstrained structural elements. By means of dynamic equilibrium considerations, the reaction of the point supports is imposed by using the Lagrange multipliers method. This yields the eigendeterminant of a constrained panel by appropriately coupling the response of a suitably large number of natural vibration modes of the corresponding unconstrained structural element.