Compressive buckling of a clamped circular plate on an elastic foundation not in attachment

A circular thin plate under radial compressive forces resting on an elastic foundation not in attachment was studied with regard to it's behavior in the 2nd mode shape.

Two regions of action are controlled by two differential equations of the fourth order which were solved in terms of the Bessel functions. The relations between the foundation modulus and the buckling load were found from two characteristic equations expressed in terms of Bessel functions.