Forced Vibrations of a Body on an Infinite Elastic Solid

Abstract

Abstract The paper considers the forced vibration of a rigid body resting on a homogeneous elastic medium of infinite surface area and constant depth which may be finite or infinite. Four modes of vibration for a body with a circular base are investigated; (a) vertical translation, (b) torsion, (c) horizontal translation, (d) rocking. For a semi-infinite medium the amplitude response can be obtained for any mass in terms of known constants of the system and two fundamental functions f1 and f2, which depend only on the exciting frequency and the properties of the medium. Close approximations to these functions have been evaluated for each mode. Experiments on an elastic model are described, the results of which are in good agreement with theoretical prediction. The behavior of a stratum of infinite area is more complex since functions f1 and f2 also depend on stratum depth. These functions have been evaluated for the torsional mode only, experimental results being given for the other modes.