### Abstract

In this paper, the scaling equation between the pseudo velocity response spectrum and the energy spectrum is proposed. Utilizing random vibration theory, the maximum response of SDOF is given as the function of power spectrum density of main part of earthquake motion. Whereas, energy spectrum is equal to Fourier amplitude spectrum smoothed by spectral window, which is clearly pointed out by Kuwamura, et al. Finally, the equation between response spectrum and energy spectrum is derived, by making connection between Fourier amplitude spectrum and power spectrum density considering the nonstationarity of earthquake motion. The proposed equation is verified not only using the artificial earthquake motions but also using the observed strong ground motions of both interplate earthquakes and inland crustal earthquakes. The equation between the peak ground acceleration/velocity and response spectrum is also proposed, which is the application of the method shown in this paper.

Original language | English |
---|---|

Pages (from-to) | 477-486 |

Number of pages | 10 |

Journal | Journal of Structural and Construction Engineering |

Volume | 74 |

Issue number | 637 |

DOIs | |

Publication status | Published - 2009 Mar |

Externally published | Yes |

### Fingerprint

### Keywords

- Duration Time of Main Earthquake Motion
- Energy Spectrum
- Magnitude
- Nonstationarity
- Response Spectrum

### ASJC Scopus subject areas

- Building and Construction
- Architecture

### Cite this

*Journal of Structural and Construction Engineering*,

*74*(637), 477-486. https://doi.org/10.3130/aijs.74.477

**Scaling equation between response spectrum and energy spectrum.** / Okano, Hajime; Nagano, Masayuki; Imamura, Akira; Tokumitsu, Ryoichi; Hijikata, Katsuichirou.

Research output: Contribution to journal › Article

*Journal of Structural and Construction Engineering*, vol. 74, no. 637, pp. 477-486. https://doi.org/10.3130/aijs.74.477

}

TY - JOUR

T1 - Scaling equation between response spectrum and energy spectrum

AU - Okano, Hajime

AU - Nagano, Masayuki

AU - Imamura, Akira

AU - Tokumitsu, Ryoichi

AU - Hijikata, Katsuichirou

PY - 2009/3

Y1 - 2009/3

N2 - In this paper, the scaling equation between the pseudo velocity response spectrum and the energy spectrum is proposed. Utilizing random vibration theory, the maximum response of SDOF is given as the function of power spectrum density of main part of earthquake motion. Whereas, energy spectrum is equal to Fourier amplitude spectrum smoothed by spectral window, which is clearly pointed out by Kuwamura, et al. Finally, the equation between response spectrum and energy spectrum is derived, by making connection between Fourier amplitude spectrum and power spectrum density considering the nonstationarity of earthquake motion. The proposed equation is verified not only using the artificial earthquake motions but also using the observed strong ground motions of both interplate earthquakes and inland crustal earthquakes. The equation between the peak ground acceleration/velocity and response spectrum is also proposed, which is the application of the method shown in this paper.

AB - In this paper, the scaling equation between the pseudo velocity response spectrum and the energy spectrum is proposed. Utilizing random vibration theory, the maximum response of SDOF is given as the function of power spectrum density of main part of earthquake motion. Whereas, energy spectrum is equal to Fourier amplitude spectrum smoothed by spectral window, which is clearly pointed out by Kuwamura, et al. Finally, the equation between response spectrum and energy spectrum is derived, by making connection between Fourier amplitude spectrum and power spectrum density considering the nonstationarity of earthquake motion. The proposed equation is verified not only using the artificial earthquake motions but also using the observed strong ground motions of both interplate earthquakes and inland crustal earthquakes. The equation between the peak ground acceleration/velocity and response spectrum is also proposed, which is the application of the method shown in this paper.

KW - Duration Time of Main Earthquake Motion

KW - Energy Spectrum

KW - Magnitude

KW - Nonstationarity

KW - Response Spectrum

UR - http://www.scopus.com/inward/record.url?scp=79954553324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954553324&partnerID=8YFLogxK

U2 - 10.3130/aijs.74.477

DO - 10.3130/aijs.74.477

M3 - Article

AN - SCOPUS:79954553324

VL - 74

SP - 477

EP - 486

JO - Journal of Structural and Construction Engineering

JF - Journal of Structural and Construction Engineering

SN - 1340-4202

IS - 637

ER -