Abstract
The dynamic response of machine foundations was one of the first problems studied in soil dynamics with results going back to the 1930s. A number of approximations and graphical results were proposed in the 60s. In this paper we present a series of approximate expressions for the natural frequencies and effective damping of rigid masses on the surface of an elastic half space subjected to both vertical and coupled horizontal-rocking harmonic excitations. The formulas are obtained using the approximate expressions for the dynamic stiffness of circular foundations suggested by Veletsos et al [1, 2] for two different values of Poisson’s ratio of the soil. For the vertical case the expressions are only a function of the mass ratio (ratio of the mass of the foundation to an effective mass of soil) and of Poisson’s ratio. For the horizontal-rocking case they depend also on the ratio of the height of the foundation to its equivalent radius (a slenderness ratio).
Highlights
The design of foundations to support heavy machinery that could induce vibrations was already recognized as an important practical problem in the 1930s giving rise to the field of Soil Dynamics
The solution for the vertical case was followed immediately by a solution for torsional vibrations. Work along these lines was continued in the following years by Reissner and Sagoci [5] and by Shekhter [6], who used the average of the displacements at the center and at the edge of the loaded area to obtain curves of dynamic amplification as a function of a dimensionless frequency and a mass ratio
A rigorous solution for the dynamic stiffness of a rigid and massless circular foundation on the surface of a linear elastic, homogeneous and isotropic half space was presented in graphical and tabular form over an extended range of frequencies by Veletsos and Wei [1] for the coupled horizontal and rocking vibrations, in 1971 an independent solution was published by Luco and Westmann [8] almost at the same time
Summary
The design of foundations to support heavy machinery that could induce vibrations was already recognized as an important practical problem in the 1930s giving rise to the field of Soil Dynamics. The solution for the vertical case was followed immediately by a solution for torsional vibrations Work along these lines was continued in the following years by Reissner and Sagoci [5] and by Shekhter [6], who used the average of the displacements at the center and at the edge of the loaded area to obtain curves of dynamic amplification as a function of a dimensionless frequency and a mass ratio. This work presents approximate explicit expressions for the natural frequencies and effective damping in each mode of a rigid mass on the surface of an elastic half space subjected to both vertical and coupled horizontal/rocking harmonic excitations These formulas are intended for preliminary estimates when designing machine foundations
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