Green's functions for continuously supported plates

The Green's functions for an infinite elastic plate, attached respectively to a Pasternak or a Kerr base model, and subjected to a concentrated force, are obtained in terms of Bessel functions. It is shown, that for each base model, depending on the plate and base parameters, the solutions may be of different form. The method of images is then utilized to generate closed form solutions for the semi-infinite and quarter plates with simply supported boundaries. Paper also presents a generalization of Bessel functions of the Kelvin type and a discussion of their properties. They were needed for the solution of some of the equations under consideration.Research supported by National Science Foundation Grant MSM-8308919.