Dynamic Analysis of an Annular Plate Resting on the Surface of an Elastic Half-Space with Distributive Properties

Abstract

This work gives a semi-analytical approach for the dynamic analysis of a plate of annular shape resting on the surface of an elastic half-space with distributive properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, the dynamic analysis of beams and plates interacting with the surfaces of elastic foundations has to date not been completely solved. To advance this work, the deflections of the plate are determined by the Ritz method, and the displacements of the surface of elastic half-space are determined by studying Green's function. The coupling of these two studies is achieved by a mixed method, which allows determination of reactive forces in the contact zone and, hence, the determination of other physical magnitudes. Natural frequencies, natural shapes, and the dynamic response of a plate due to external harmonic excitation are determined. Validation with a Winkler problem illustrates the distributive property effects on the results of the dynamic analysis.