General solutions and fundamental solutions of varied orders to the vibrational thin, the Berger, and the Winkler plates

In this note, we derive the general and the fundamental solutions of varied orders of vibrational thin plate, Berger plate, and Winkler plate. These solutions are of important use in the multiple reciprocity BEM, dual reciprocity BEM, boundary particle method, boundary knot method, and a variety of radial basis function techniques.