Dynamic analysis of isotropic composite plates using a layerwise theory

The paper is concerned with small amplitude vibrations of moderately thick composite plates. Polygonal and simply supported plates of three asymmetrically arranged layers in perfect bond are considered. The homogeneous layers are assumed to consist of isotropic linear elastic materials. The Mindlin¯Reissner kinematic assumptions are implemented separately to each layer, and as such model both the global and local elastic response of composite plates. The continuity of the transverse shear stress across the interfaces is prescribed according to Hookeʹs law. For plates composed of layers with a uniform ratio of mass density to shear modulus and a common Poissonʹs ratio the lateral deflection can be calculated independently from the in-plane displacements. It is shown that the lateral deflection is governed by a boundary value problem of the fourth order. Alternatively, by neglecting the longitudinal as well as rotary inertia the complex problem reduces to the simpler case of a homogenized shear-deformable plate with effective stiffness and corresponding set of boundary conditions. The theory is applied to statically and dynamically loaded rectangular simply supported composite plates with various dimensions and material properties.