Vibration of viscoelastic foundations

Abstract

Simple approximate solutions are presented for the steady‐state response of a massless, rigid disk, which is supported at the surface of a linear viscoelastic halfspace and is excited by a harmonically varying horizontal or vertical force, or by a harmonically varying moment about an axis in the plane of the disk. The halfspace is idealized either as a standard Voigt solid or as a constant hysteretic solid. The solution for the massless disk is then applied to the analysis of foundations with mass, and for each mode of excitation, comprehensive numerical data are presented to illustrate the effects of viscoelastic action on the response of both the massless disk and of foundations with mass It is shown that the principal effects of material damping are to increase the damping capacity of the foundation and to reduce its ‘natural’ frequency. In the mathematically equivalent representation of the elastically supported massless disk as a spring‐dashpot combination without mass, it is shown that the effective stiffness of the spring may become negative over significant ranges of the exciting frequency, and that it is preferable to model the disk‐halfspace system as an oscillator with mass, taking its spring constant equal to the static stiffness of the original system.

Performance-based seismic design of flexible-base multi-storey buildings considering soil–structure interaction

“…In this study, the soil material damping ratio x g =5% was specified at the lowest Eigen-frequency w 0 of an SSI system, which can be calculated iteratively according to Veletsos and Nair [23] and Luco and Lanzi [24]. Frequency-dependent impedance functions proposed by Veletsos and Verbic [25] were used to derive w 0 , which was solved iteratively by increasing the frequency of vibration from zero (i.e. static condition) to 10V s /r until both frequencies were equal within 0.1 percent (i.e.…”

Efficient Modelling of Wind Turbine Foundations

“…Examples include analytic, semi-analytic or semi-empirical methods as proposed by Luco & Westmann (1971), Luco (1976), Krenk & Schmidt (1981), Wong & Luco (1985), Mita & Luco (1989), Wolf (1994) and Vrettos (1999) as well as Andersen & Clausen (2008). Especially, torsional motion of footings was studied by Novak & Sachs (1973) and Veletsos & Damodaran Nair (1974) as well as Avilés & Pérez-Rocha (1996). Rocking and horizontal sliding motion of footings was analysed by Veletsos & Wei (1971) and Ahmad & Rupani (1999) as well as Bu & Lin (1999).…”

Seismic Soil-Structure Interaction in Buildings. II: Empirical Findings

“…One methodology is termed the ''modified Veletsos'' (MV) formulation, because it is based on the impedance function in Veletsos and Verbic (1973) and the derivations for and T/T in Veletsos and Nair (1975) for a single-degree-of-freedom 0 structure supported on a rigid circular foundation resting on the surface of a homogeneous viscoelastic half-space. The modified terms refers to adjustments to the impedance function required to account for the effects of nonuniform soil profiles and foundation embedment, shape, and flexibility.…”