Free-vibration analysis of a three-dimensional soil-structure system

Abstract

A procedure which involves a non-linear eigenvalue problem and is based on the substructure method is proposed for the free-vibration analysis of a soil-structure system. In this procedure, the structure is modelled by the standard ÿnite element method, while the unbounded soil is modelled by the scaled boundary ÿnite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam-foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also veriÿed by the Fourier transform of the impulsive response calculated in the time domain by the three-dimensional soil-structure-wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are signiÿcantly di erent due to the di erent deÿnition of damping ratio. This study shows that although the classical mode-superposition method is not applicable to a soil-structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil-structure system.

Dynamic wave–soil–structure interaction analysis in the time domain

“…If both seismic excitation and externally applied transient loading are considered, the equation of motion of the structure in the time domain can be expressed as [2] M ss M sb…”

“…In that study, the scattering and diffraction of seismic waves by various three-dimensional surface irregularities were studied in detail, and the numerical results obtained were in good agreement with those given by others. In a later paper by Wegner and Zhang [2], DSSIA-3D was applied to obtain the dynamic response of a spherical cavity, embedded in full-space, subjected to seismic waves. In that study, the numerical results were compared to the analytical solutions, with excellent agreement.…”

“…The novel three-dimensional dynamic soil-structure interaction procedure (DSSIA-3D) [1,2] uses the scaled boundary finite-element method to model the unbounded soil while the structure is modeled using standard finite-element method. In this numerical procedure, approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are implemented in the scaled finite-element method resulting in an order of magnitude reduction in the required computational effort when compared to other methods.…”

A Novel Calculation Method of Hydrodynamic Pressure Based on Polyhedron SBFEM and Its Application in Nonlinear Cross-Scale CFRD-Reservoir Systems

“…Initially, SBFEM was conceived for the field of computational elasticity [2][3][4]. As SBFEM became more mature, Zhang and Wegner [5,6] spearheaded SBFEM-based dynamic coupling analysis between the threedimensional (3D) infinite foundation and structure, and in their studies, the substructure method was used to improve computational efficiency and analyze the wave motion of seismic waves. Subsequently, further details of the dynamic interaction between structure and foundation were studied [7][8][9][10] by SBFEM, which automatically satisfied the infinite radiation condition.…”

Dynamic Properties of OffshoreWind Turbine Foundations

“…Yazdchi et al (1999) studied the response of dam-foundation interaction for seismic loads including the effects of pre-seismic loads such as water pressure and self weight of the dam. A similar structure was investigated by Touhei and Ohmachi (1994) and Wegner and Zhang (2001), who evaluated the natural modes of vibration of a dam-foundation system. For different geometries of circular foundations embedded in a non-homogeneous half-space, Doherty and Deeks (2003) used a frequency-domain FE/BE approach to obtain semi-analytical stiffness coefficients for the footings subjected to vertical, horizontal, rocking and torsional loads.…”