Eigenstrain induced vibrations of composite plates

The paper is concerned with eigenstrain induced small amplitude vibrations of moderately thick composite plates. In case of thermal shock loading such eigrnstrains are imposed as thermal strains. Within a multiple field approach. thermal strains: piezoelectrically induced strains. as well as additional fields of strains that are due to inelastic deformations are interpreted as eigenstrains acting in the associated linear elastic background structure. Polygonal simply supported composite plates with three asymmetrically arranged layers in perfect bond are considered. The homogeneous layers consist of dissimilar linear elastic isotropic materials. The Mindlin-Reissner kinematic assumptions are implemented separately to each layer. The continuity of the transverse shear stress across the interfaces is prescribed according to Hooke's law. For plates composed of layers with a uniform ratio of mass density to shear modulus and a common Poissons 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 rotatory inertia the complex problem reduces to the simpler case of a homogenized shear-deformable plate with effective stiffness, a corresponding set of boundary conditions and effective eigenstrain resultants. The theory is applied to rectangular simply supported composite plates of various dimensions.