Basic Response Functions for Elastic Foundations

Approximate, close-form expressions are presented for the response to both harmonic and impulsive excitations of a massless, circular, rigid foundation which is supported at the surface of an elastic half space and is excited horizontally, vertically, or in rocking motion. The impulse response functions considered include: (1) functions for the displacements of the disk due to unit impulsive forces; and (2) functions for the forces necessary to produce unit impulsive displacements. The functions of the first type are also evaluated numerically, and the results are used to assess the accuracy of the analytical approximations proposed. Some comparisons are also made with results obtained for a viscously-damped, simple oscillator with or without mass. With the impulse response functions presented, analyses of the transient response of foundations and foundation-structure systems can be carried out directly in the time domain. This approach may be more efficient or of wider applicability in specific applications than the corresponding frequency-domain approach.