Analytical solution to dynamic buckling of a rectangular thin plate with one edge clamped and other three edges simply supported

Based on the twin-characteristic-parameter method and stress wave theory, dynamic buckling displacements of a rectangular thin plate with one edge clamped and other three edges simply supported subjected to axial impact in-plane were obtained analytically by solving the dynamic balance equations of a plate with a supplementary restraint-equation in compressive wave front. In the dynamic buckling process of the rectangular thin plate, relations of its thickness-width rate, the amplitude of impulsive loads, buckling modes and critical buckling length were found out. The results indicated that for the existence of transverse inertia effect, the critical load of dynamic buckling is much bigger than that of static buckling.