Body Wave Excitation of Embedded Hemisphere

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Abstract
Solutions of three-dimensional vibrations of an embedded hemispherical foundation are presented for excitation by incident plane P, SV, and SH waves with arbitrary angles of incidence. The effects of embedment are illustrated by comparing the motion of the embedded hemispherical foundation with those of a rigid disc bonded to a half space of equal radius and excited by the same waves. The impedence matrix and the foundation motion are analyzed and compared with similar and reLated approximate solutions. In the context of Fourier synthesis, the results can be viewed as representing the transfer functions for the forces and motions of the foundation. For arbitrary transient excitation which can be represented by plane body waves, the results can be used to calculate the transient motion of the foundation.

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