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

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 so il-structure system. In this procedure, the structure is modelled by the st andard finite element method, while the unbounded soil is modelled by the s caled boundary finite element method. The fundamental frequency, and the co rresponding 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 ver ified by the Fourier transform of the impulsive response calculated in the time domain by the three-dimensional soil-structure-wave interaction analys is procedure proposed in our previous paper. The fundamental frequency obta ined 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 si gnificantly different due to the different definition of damping ratio. Thi s study shows that although the classical mode-superposition method is not applicable to a soil-structure system due to the frequency dependence of th e radiation damping, it is still of interest in earthquake engineering to e valuate the fundamental frequency and the corresponding radiation damping r atio of the soil-structure system. Copyright (C) 2001 John Wiley & Sons, Lt d.