Effective time‐domain soil‐structure interaction analysis based on FFT algorithm with causality condition

Abstract

SUMMARYWe propose an effective and reliable time-domain substructure technique which takes soil-structure interaction effects into account and uses the flexibility coefficients of unbounded soil obtained in the frequency domain. Compared with previous methods, the frequency points t o calculate flexibility coefficients, and computational loads in the calculation of time-domain interaction forces, are reduced.In the formulation, we have assumed the flexibility coefficient to be a periodic function, obtained within the bandlimited frequency range, which also includes the predominant frequencies of the structure and incident wave. Then we simulate the periodic flexibility coefficients using discrete impulse responses in the time-domain analyses. However, the real and imaginary parts of the bandlimited flexibility coefficients do not form a Hilbert transform pair; the discrete impulse responses should be modified to be causal for the time-domain analyses. We present various discrete impulse responses which have been obtained from only the real part, only the imaginary part and from both the real and imaginary parts of the frequency-domain flexibility coefficients by FFT with causality conditions. Through a numerical example the relationship between the modified discrete impulse responses and the validity of the time-domain substructure method is presented.

A practical method to transform frequency dependent impedance to time domain

“…For the purpose of preventing this, a method for computing either the real part or the imaginary part from the other part by carrying out the Hilbert transform is often used [5]. However, this method causes a distortion of the original function.…”

“…Meek [3] showed the general version of the recursive method and Motosaka et al [4] indicated the applicability of the ARMA type recursive formula by means of developing the aforementioned method. Hayashi et al [5] investigated the formulation of the transform method using the fast Fourier transform with consideration to the causality condition.…”

Application of a Highly Reduced One- Dimensional Spring-Dashpot System to Inelastic SSI Systems Subjected to Earthquake Ground Motions

“…The origins of this method date back to Wolf & Obernhuber, 1985, who developed a numerical method in the time domain in which the impulse response obtained from dynamic soil stiffness by using inverse Fourier transform was applied to the response analysis. Since this method was first developed in the 1980s, many transform methods in the time domain have been proposed and improved to overcome difficulties in various frequency dependencies in IFs (Wolf & Motosaka, 1989;Meek, 1990;Motosaka & Nagano, 1992;Hayashi & Katsukura, 1990). Nakamura (2006a;2006b;2008a;2008b) has developed various sophisticated transform methods that can deal with strong frequency dependency in IFs, non-causal impedance with large hysteretic damping, and soil nonlinearity.…”

Earthquake response analysis in the time domain for 2D soil–structure systems using analytical frequency‐dependent infinite elements

“…This method, which does not require fundamental solution, has been successfully used in coupling with ÿnite elements and applied for three-dimensional soil-structure interactions in the time domain. Another method is the one using the transformation of the dynamic sti ness matrix into the terms in time the domain [16]. However, the dynamic sti ness matrix for the far-ÿeld region is usually obtained numerically at each frequency.…”