Consider a simply supported square plate subjected to a uniformly distributed compressive in-plane loading, N per unit length. Show that that the critical in-plane compression loading, at the edges of...

Consider a simply supported square plate subjected to a uniformly distributed compressive in-plane loading, N per unit length. Show that that the critical in-plane compression loading, at the edges of the square plate, such that the first natural frequency of vibration is equal to zero, is given by