Numerical modelling of parametric instability problem for composite plate using finite element method

Abstract

The application of laminated sandwich composite in machine structures is attractive due to the low specific and tailorable properties of the composites. As such a study on the parametric instability that often occurs in machine structures should be crucially conducted on composite plates. In this paper, finite element method (FEM) has been used to model laminated composite plate subjected to periodic compressive loading for the parametric instability analysis. The FEM formulation is based on the first order shear deformation theory. Eight noded serendipity element that requires 5 degrees of freedom per node is used in this study. The developed Mathieu-Hill type equation that represents the parametric instability of the composite plate has been solved using the Bolotin's method that reduces the Mathieu-Hill equation to a couple of eigen-value problems. The FEM source codes have been developed to determine the instability charts for several configurations of composite plates. While the formulation and codes have been found to give results that agree well with past results, it has been also been found that as the static load factor is increased, the frequency center for dynamic instability region is shifted to the left while the degree of instability is increased.