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Vertical motion of rigid footings

Lysmer, John

Vicksburg, Miss. : Waterways Experiment Station, Contract report - U.S. Army Engineer Waterways Experiment Station ; no. 3-115., 1965, PDF (2.4 MB) (485 L9 1965)

This work deals with the vertical mode of vibration of a rigid circular footing resting on a plane soil surface and excited by a vertical time-dependent force in the axis of symmetry. It is assumed that the subsoil can be considered as a perfectly elastic, isotropic, and homogeneous half space. First an approximate theoretical solution is developed for the steady-state motion of the above half-space model. This solution differs from previously published solutions in that it includes all frequencies of excitation. It is then shown how the transient response due to a pulse-type loading can be calculated from the steady-state solution by a simple Fourier technique, and a computer program using this technique is presented. Parallel with the above development it is shown that the elastic half-space model behaves very similarly to a simple damped oscillator,and the author proposes the use of a simplified analog of the mass-spring-dashpot type for practical calculations. The above theoretical results are supported by the presentation of both steady-state and impact tests performed by other researchers.

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