On the dynamic instability of a rectangular plate with one free edge

The problem of dynamic stability of a rectangular plate is considered. It is supposed that two opposite sides of the plate are freely supported, the third side is either hingedly supported or rigidly clamped, and the fourth side is free and carries a finite mass. The plate is compressed by a tracking load applied to the last side. The dependence of the critical load on the relative length of the plate, i.e., the distance between sides with different conditions, is obtained.