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Structural Engineering and Mechanics
  Volume 31, Number 2, January30 2009 , pages 211-223
DOI: https://doi.org/10.12989/sem.2009.31.2.211
 


On the extended period of a frequency domain method to analyze transient responses
Kui Fu Chen, Qiang Zhang, Sen Wen Zhang

 
Abstract
    Transient response analysis can be conducted either in the time domain, or via the frequency domain. Sometimes a frequency domain method (FDM) has advantages over a time domain method. A practical issue in the FDM is to find out an appropriate extended period, which may be affected by several factors, such as the excitation duration, the system damping, the artificial damping, the period of interest, etc. In this report, the extended period of the FDM based on the Duhamel\'s integral is investigated. This Duhamel\'s integral based FDM does not involve the unit impulse response function (UIRF) beyond the period of interest. Due to this fact, the ever-lasting UIRF can be simply set as zero beyond the period of interest to shorten the extended period. As a result, the preferred extended period is the summation of the period of interest and the excitation duration. This conclusion is validated by numerical examples. If the extended period is too short, then the front portion of the period of interest is more prone to errors than the rear portion, but the free vibration segment is free of the wraparound error.
 
Key Words
    transient response; frequency domain method; fast fourier transform (FFT); laplace transform; Duhamel
 
Address
Kui Fu Chen; College of Sciences, China Agricultural University, Beijing 100083, P.R. China
Qiang Zhang; Architecture Engineering School, Shanghai Normal University, Shanghai 201418, P.R. China
Sen Wen Zhang; The Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P.R. China
 

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