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Kaibai Liu

Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering

First Advisor

Hamid R. Hamidzadeh


The principal objective of this thesis is to study the dynamics of a rectangular foundation subjected to different types of harmonic loadings. The foundation is assumed to be a rigid block with a uniform mass distribution. The medium on which the foundation is founded is modeled as a homogeneous, isotropic, continuous and elastic semi-infinite body (elastic half-space). An effort is made to develop procedures and computing algorithms to tackle practical problems arising in the field. In order to comprehend the problem of soil structure interaction, the general equations for waves travelling in the elastic medium were formulated, and transmission of those elastic waves are discussed. Of most interest is the study of the Rayleigh wave, which has a great significance on the surface of the elastic half-space. Also, Lamb's problem is described which is the starting stage to address soil-structure interaction problems. An analytical solution to the Lamb's problem is provided and the final expression for the displacements of a point on the surface of the half-space are computed numerically. Particular attention is paid to the methodology established by Hamidzadeh. The main procedure to obtain the displacement functions under the consideration of a uniform displacement distribution at each discretized subregion is described in detail. The extension of the method to the problem of a massive rectangular foundation is also included. Many techniques established by the elastic half-space theory provide a bridge between the simple mass-spring-dashpot system and the analysis of the actual response of the foundation due to dynamic loads. Because of the advantage in the mathematical treatment, the mass-spring-dashpot system, or so called the lumped parameter system, has been widely applied in various dynamic analyses of foundations. The equivalent stiffnesses and damping coefficients for different pure modes of vibration are considered in detail. The results are further applied to the case of three-dimensional (six-degree of freedom) vibration for a square foundation. Also, comparisons are presented between the lumped parameter method and other theoretical methods. The dynamic response of a rectangular subjected to coupled horizontal and footing rocking vibration is investigated and some design guidelines are provided. The computed results are compared with other available methods as well as experimental results. The deviations between them are studied and justified.

Library of Congress Subject Headings

Foundations -- Vibration

Elastic analysis (Engineering)

Structural analysis (Engineering)



Number of Pages



South Dakota State University