Natural frequencies of thick, layered composite plates

Abstract

We develop analyses and numerical calculations for the free vibration of simply supported, thick, layered composite plate strips composed of off-axis lamina. It is assumed that each layer of the composite plate is of arbitrary thickness and possesses up to monoclinic symmetry. Formal solutions are obtained for the individual layers which relate the field variables at the upper and lower layer surfaces. Here, linear transformations are used to refer the anisotropy of each layer to a global coordinate system. The solution of the characteristics for the total system proceeds by utilizing the matrix transfer method, which relies on satisfying appropriate interfacial conditions across the constituents, and results in a third-order eigenproblem. The order of the free vibration eigenproblem of the layered plate strip is thereby rendered independent of the number of layers in the composite plate. Numerical illustrations are given in the form of normalized natural frequency vs nondimensionalized mode number. The effect of the plate's microstructure on its vibration characteristics is investigated by examining changes in natural frequencies for various laminate lay-ups and material combinations.