Dynamic stability of a thin plate subjected to bi-axial edged loads

Abstract

The first dynamic stability of a thin rectangular plate made from linear elastic material and subjected to a bi-axial time dependent load is discussed in this study. The plate carries a combination of loads that are changing linearly with respect to the length of its edges. It is also supposed that its boundary conditions on the edges are simply supported. Relevant inertia, elastic stiffness, and stability matrices are derived by applying Finite Difference Method from a differential motion equation of the plate. Subsequently, Mathieu-Hill equation form is obtained for the plate and the first dynamic stability boundaries of the plate are elaborated for using specified load parameters.