A practical method to transform frequency dependent impedance to time domain

Nakamura, Naohiro

doi:10.1002/eqe.520

Cited by 35 publications

(23 citation statements)

References 10 publications

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“…This figure shows that the results in each case almost correspond to each other as a whole, but some differences are discernible in lowfrequency ranges. This is because the differences in the time-delay components of the stiffness term for the impulse response have a great effect on the low-frequency range of the recovered impedance as shown in Reference [1]. Figure 6(b) expands the frequency range 0-4 Hz in Figure 6(a).…”

Section: Investigation Using Greatly Noncausal Impedance (In the Casementioning

confidence: 93%

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Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only

Nakamura

2008

Earthq Engng Struct Dyn

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SUMMARYThe author has studied the transform method of complex stiffness, which is strongly dependent on frequency, to the time domain. In this paper, new transform methods that use only the real part or the imaginary part data are proposed. By applying them to example problems, it is confirmed that the accuracy of the proposed methods is almost high in both causal and noncausal cases. These methods can also be thought as a standby for the Hilbert transform, because the undefined part is easily calculated by the recovering complex function from the obtained impulse response.

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Section: Investigation Using Greatly Noncausal Impedance (In the Casementioning

confidence: 93%

“…The author has studied the transform method of complex stiffness, which is strongly dependent on frequency, to the time domain [1] and proved the applicability of an approximate transform method of the noncausal impedance with large hysteretic damping [2].…”

Section: Introductionmentioning

confidence: 99%

Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only

Nakamura

2008

Earthq Engng Struct Dyn

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Saitoh¹

2012

Advances in Geotechnical Earthquake Engineering - Soil Liquefaction and Seismic Safety of Dams and Monuments

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“…During a severe earthquake the building and its surrounding soil exhibit nonlinear behaviour. It is thus desirable to be able to use this boundary in the time domain also.The author has previously studied how to transform TB to the time domain with high accuracy and ease in cases where the dynamic stiffness has a strong frequency dependency [3,4]. As part of these efforts, the author transformed TB of the 2-dimensional in-plane problem, which is equivalent to FLUSH, into the time domain, and showed that high-accuracy analysis is possible in the same manner as with the frequency domain.…”

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confidence: 99%

Earthquake Response Analyses of Soil-Structure Interaction System Using Nonlinear Energy Transmitting Boundary

Nakamura¹

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The energy-transmitting boundary, which is used in the well-known FEM program FLUSH, is a quite efficient technique for the earthquake response analysis of buildings considering soil-structure interaction. However, it is applicable only in the frequency domain. The author has studied and proposed methods for transforming frequency dependent soil impedance into the time domain.In the previous paper, the author proposed an earthquake response analysis method using the energy transmitting boundary in the time domain using the transform method, because the kernel of the boundary is the frequency dependent impedance full matrix. Then, an earthquake response analysis with a nonlinear building using the boundary was carried out, and the accuracy and the efficiency of the boundary were confirmed. In that analysis, the inner field (the region inside the boundary) could be treated as the nonlinear system, but the free field (the region outside the boundary) and the boundary were treated as the linear system.Contrary to this, in this paper, the nonlinear transmitting boundary is proposed. By using it, all of the inner field, the free field and the boundary itself can be treated as the nonlinear system. The boundary impedance matrix is calculated in the frequency domain corresponding to the condition of the free field at the specific times. Then, these impedance matrices are transformed to the impulse response matrices in the time domain. In the nonlinear response analysis of the total system, the transmitting boundary at each time step is obtained by interpolation of these impulse response matrices between the specific times. Then, example earthquake response analyses were performed using a practical soil and building model to evaluate the soil-structure interaction effect. The response accuracy was compared with the cases of viscous boundary, which is the most common and representative boundary in the time domain. It was shown that the area of the inner field can be greatly reduced by using the proposed method because the accuracy of the boundary is quite high. Therefore, it was confirmed that the proposed method is effective. 812Naohiro Nakamura INTRODUCTIONThe energy transmitting boundary (hereinafter referred to as TB), which is used in FLUSH [1] and ALUSH [2], is a side wave boundary that is highly accurate and is highly effective. These programs developed in the 1970s are still utilized today as powerful tools in design study for architecture and civil engineering. However, TB has been formulated in the frequency domain, and can only perform linear analysis and equivalent linear analysis within the frequency domain. During a severe earthquake the building and its surrounding soil exhibit nonlinear behaviour. It is thus desirable to be able to use this boundary in the time domain also.The author has previously studied how to transform TB to the time domain with high accuracy and ease in cases where the dynamic stiffness has a strong frequency dependency [3,4]. As part of these efforts, the author transformed...

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A practical method to transform frequency dependent impedance to time domain

Cited by 35 publications

References 10 publications

Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only

Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only

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

Earthquake Response Analyses of Soil-Structure Interaction System Using Nonlinear Energy Transmitting Boundary

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