Analysis of machine foundation vibrations: State of the art

In this study of the dynamics of building-soil interaction, the soil is modeled by a linear elastic half-space, and the building structure by an n-degree-of-freedom oscillator. Both earthquake response and steady-state response to sinusoidal excitation are examined. By assuming that the interaction system possesses n + 2 significant resonant frequencies, the response of the system is reduced to the superposition of the responses of damped linear oscillators subjected to modified excitations. The results are valid even though the interaction systems do not possess classical normal modes. For the special cases of single-story systems and the first modes of n-story systems, simplified approximate formulas are developed for the modified natural frequency and damping ratio, and for the modified excitation. Example calculations are carried out by the approximate and more exact analysis for one-story, two-story and ten-story interaction systems.

The results show that interaction tends to decrease all resonant frequencies, but that the effects are often significant only for the fundamental mode for many n-story structures and are more pronounced for rocking than for translation. If the fixed-base structure has damping, the effects of interaction on the earthquake responses are not always conservative, and an increase or decrease in the response can occur, depending on the parameters of the system.

Dynamics of building-soil interaction

Early history of soil–structure interaction

http://ssi.civil.ntua.gr/downloads/journals/2006-SDEE_Footings%20under%20seismic%20loading_Analysis%20and%20design%20issues%20with%20emphasis%20on%20bridge%20foundations.pdf

Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations

Dynamic response of rigid foundations of arbitrary shape

It is the purpose of the paper to present the dynamic compliances of a circular footing resting on an elastic half-space for a wide range of dimensionless frequency. Numerical results have been presented for the torsional, vertical, rocking and horizontal oscillations of a rigid disc placed on an elastic half-space, as well as for the coupling terms between the rocking and horizontal oscillations. The corresponding compliances, the stress distributions under the disc, and the Rayleigh wave part of the far-field displacements have been evaluated. It is hoped that these results will prove to be useful in the design of foundations for vibrating machinery and in the study of soil structure interaction.

Juan E. Luco

Papers

Dynamic Response of Circular Footings