Dynamic analysis of a plate resting on elastic half-space with distributive properties

This work gives a semi-analytical approach for the dynamic analysis of a plate resting on 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 foundation are determined by studying Green's function. The coupling of these two studies is achieved by a mixed method, known in the theory of elasticity as Zhemochkin’s method, which allows determination of reactive forces in the contact zone and, hence, the determination of other physical magnitudes. The obtained solutions can be applied to study the dynamic interaction between soils and structures and to assess numerical computations through various numerical methods programs. 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.