Parametric Instability of Laminated Composite Plates Using Third Order Shear Deformation Theory

Abstract

Parametric instability as compared to force resonance may occur in a structure when the frequency of loading is at a fraction of the natural frequency of the structure. As such the structure may experience fatigue failure due to parametric instability merely at loading less than its critical load. In this paper, parametric instability analysis of composite plate subjected to periodic compressive loading has been conducted using finite element method (FEM). The FEM formulation is based on the third order shear deformation theory. The Mathieu-Hill type equation that described the parametric instability of the composite plate was developed using the Hamilton’s principle. This equation was solved using the Bolotin’s method that reduces the Mathieu-Hill equation to a couple of eigen-value problems. Using the developed FEM source codes, the instability chart or the Strut-Ince diagrams were drawn to show the instability regions for several cases of composite types and parameters. The results of the dynamic instability region were validated with the results from past literatures. It was found that as the static load parameter is increased, the center for dynamic instability region is shifted to the left and in the case of symmetric angle-ply composite plate, the orientation angle of θ = 45° gives the highest frequency at the center of the instability chart.