Dynamic instability of composite laminated plates

Abstract

Dynamic instability in a laminated composite plate is studied using the finite element technique. The governing equations are derived based on the first order shear deformation theory with a linear strain-displacement relationship. The regions of instability for the resulting set of coupled Mathieu equations are obtained using a method of simultaneous diagonalization. Boundary frequencies generated using a first subdeterminant approximation to the infinite determinant are compared with those obtained by using the more accurate second subdeterminant as well as with frequencies from an analytical solution. These values are verified by checking the nature of responses near the boundaries between stability and instability. Results are presented for plates with different laminations, boundary conditions, thicknesses, number of layers, etc. Some unstable regions for a damped plate are also shown. Results from the first order plate theory are compared with those from a higher order shear deformation theory.