On Natural Vibrations and Waves in Laminated Orthotropic Plates

A solution method is presented for studying the vibrations of a laminated plate composed of an arbitrary number of bonded elastic, orthotropic layers. The analysis is carried out within the framework of linear elasticity for plane-strain behavior. The essence of the method is a discretization of the plate into arbitrarily large number of laminas, each of which comprise a separate entity. An approximate displacement field is assumed for each lamina and is characterized by a discrete number of generalized coordinates at the laminar bounding planes and at its midsurface. An algebraic eigenvalue problem results, whose solution yields the frequencies and modal displacement patterns, the 10 lowest which are determined. Stresses are calculated in a straightforward manner from eigenvectors. A homogeneous isotropic plate is studied to ascertain the accuracy and effectiveness of this method and examples on homogeneous and laminated orthotropic plates are given to offer some insight on their physical behavior.