Structural Engineering and Mechanics

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On the extended period of a frequency domain method to analyze transient responses

  • Chen, Kui Fu (College of Sciences, China Agricultural University) ;
  • Zhang, Qiang (Architecture Engineering School, Shanghai Normal University) ;
  • Zhang, Sen Wen (The Institute of Applied Mechanics, Jinan University)
  • Received : 2006.10.25
  • Accepted : 2008.12.17
  • Published : 2009.01.30
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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.

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References

  1. Adhikari, S. (2002), 'Dynamics of nonviscously damped linear systems', J. Eng. Mech., 128(3), 328-339 https://doi.org/10.1061/(ASCE)0733-9399(2002)128:3(328)
  2. Aleyaasin, M., Ebrahimi, M. and Whalley, R. (2001), 'Flexural vibration of rotating shafts by frequency domain hybrid modelling', Comput. Struct., 79(3), 319-331 https://doi.org/10.1016/S0045-7949(00)00133-4
  3. Barkanov, E. (1999), 'Transient response analysis of structures made from viscoelastic materials', Int. J. Numer. Meth. Eng., 44(3), 393-403 https://doi.org/10.1002/(SICI)1097-0207(19990130)44:3<393::AID-NME511>3.0.CO;2-P
  4. Beskos, D.E. and Narayann, G.V. (1983), 'Dynamic response of frameworks by numerical laplace transform', Comput. Method. Appl. M., 37, 289-307 https://doi.org/10.1016/0045-7825(83)90080-4
  5. Chen, K.F. and Zhang, S.W. (1999), 'DFT acceleration and its application in non-stationary random vibration calculation', Chinese J.Vib. Eng., 12(1), 91-96
  6. Chen, K.F. and Zhang, S.W. (2006), 'On the convergence and causality of a frequency domain method for dynamic structural analysis', Acta Mech. Sinica, 22(2), 162-169 https://doi.org/10.1007/s10409-006-0098-2
  7. Chen, K.F. and Zhang, S.W. (2008), 'On the Impulse response precursor of an SDOF ideal linear hysteretic damper', J. Sound Vib., 312(4-5), 576-583
  8. Cooley, J.W. and Tukey, J.W. (1965), 'An algorithm for the machine calculation of complex fourier series', Math. Comput., 19(90), 297-305
  9. Dumont, N.A. and Oliveira, R.D. (2001), 'From frequency-dependent mass and stiffness matrices to the dynamic response of elastic systems', Int. J. Solids Struct., 38(10-13), 1813-1830 https://doi.org/10.1016/S0020-7683(00)00137-2
  10. Durbin, F. (1974), 'Numerical inversion of Laplace transforms: an efficient improvement to Duber and Abate's method', Comput. J., 17(4), 371-376 https://doi.org/10.1093/comjnl/17.4.371
  11. Genes, M.C. and Kocak, S. (2005), 'Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model', Int. J. Numer. Meth. Eng., 62(6), 798-823 https://doi.org/10.1002/nme.1212
  12. Gupta, A.K., Hassan, T. and Gupta, A. (1996), Time and frequency domain analyses of single-degree-of-freedom systems', Nuclear Eng. Des., 167(1), 1-5 https://doi.org/10.1016/S0029-5493(96)01286-1
  13. Hall, J.F. (1982), 'FFT algorithm for structural dynamics', Earthq. Eng. Struct. Dyn., 10(6), 797-811 https://doi.org/10.1002/eqe.4290100605
  14. Hall, J.F. and Beck, J.L. (1993), 'Linear System Response by DFT: Analysis of a recent modified method', Earthq. Eng. Struct. Dyn., 22(7), 599-615 https://doi.org/10.1002/eqe.4290220705
  15. Humar, J.L. and Xia, H. (1993), 'Dynamic response analysis in the frequency domain', Earthq. Eng. Struct. Dyn., 22(1), 1-12 https://doi.org/10.1002/eqe.4290220102
  16. Humar, J.L., Bagchit, A. and Xia, H. (1998), 'Frequency domain analysis of soil-structure interaction', Comput. Struct., 66(2-3), 337-351 https://doi.org/10.1016/S0045-7949(97)00068-0
  17. Inaudi, J.A. and Kelly, J.M. (1995), 'Linear hysteretic damping and the Hilbert transform', J. Eng. Mech., ASCE, 121(5), 626-632 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:5(626)
  18. Kargarnovin, M. and Younesian, D. (2004), 'Dynamics of Timoshenko beams on Pasternak foundation under moving load', Mech. Res. Commun., 31(6), 713-723 https://doi.org/10.1016/j.mechrescom.2004.05.002
  19. Kausel, E. and Roeosset, J.M. (1992), 'Frequency domain analysis of undamped systems', J. Eng. Mech., ASCE, 118(4), 721-734 https://doi.org/10.1061/(ASCE)0733-9399(1992)118:4(721)
  20. Kim, D.K. and Yun, C.B. (2003), 'Earthquake response analysis in the time domain for 2D soil-structure systems using analytical frequency-dependent infinite elements', Int. J. Numer. Meth. Eng., 58(12), 1837-1855 https://doi.org/10.1002/nme.838
  21. Liu, S.W. and Huang, J.H. (2003), 'Transient dynamic responses of a cracked solid subjected to in-plane loadings', Int. J. Solids Struct., 40(18), 4925-4940 https://doi.org/10.1016/S0020-7683(03)00276-2
  22. Maeso, O., Aznarez, J.J. and Dominguez, J. (2004), 'Three-dimensional models of reservoir sediment and effects on the seismic response of arch dams', Earthq. Eng. Struct. Dyn., 33(10), 1103-1123 https://doi.org/10.1002/eqe.392
  23. Makris, N. and Zhang, J. (2000), 'Time-domain viscoelastic analysis of earth structures', Earthq. Eng. Struct. Dyn., 29(6), 745-768 https://doi.org/10.1002/(SICI)1096-9845(200006)29:6<745::AID-EQE937>3.0.CO;2-E
  24. Moulinec, H. and Suquet, P. (2003), 'Comparison of FFT-based methods for computing the response of composites with highly contrasted mechanical properties', Physica B, 338(1-4), 58-60 https://doi.org/10.1016/S0921-4526(03)00459-9
  25. Polyzos, D., Tsepoura, K.G. and Beskos, D.E. (2005), 'Transient dynamic analysis of 3-D gradient elastic solids by BEM', Comput. Struct., 83(10-11), 783-792 https://doi.org/10.1016/j.compstruc.2004.11.001
  26. Siqueira Meirelles, P. and Arruda, J.R.F. (2005), 'Transient response with arbitrary initial conditions using the DFT', J. Sound Vib., 287(3), 525-543
  27. Song, C.M. and Wolf, J.P. (2000), 'The scaled boundary finite-element method - a primer: Solution procedures', Comput. Struct., 78(1-3), 211-225 https://doi.org/10.1016/S0045-7949(00)00100-0
  28. Tsai, H.C. and Lee, T.C. (2002), 'Dynamic analysis of linear and bilinear oscillators with rate-independent damping', Comput. Struct., 80(2), 155-164 https://doi.org/10.1016/S0045-7949(01)00169-9
  29. Veletsos, A.S. and Ventura, C.E. (1984), 'Efficient analysis of dynamic response of linear-systems', Earthq. Eng. Struct. Dyn., 12(4), 521-536 https://doi.org/10.1002/eqe.4290120408
  30. Veletsos, A.S. and Ventura, C.E. (1985), 'Dynamic analysis of structures by the DFT', J. Eng. Mech., ASCE, 111(12), 2625-2642 https://doi.org/10.1061/(ASCE)0733-9445(1985)111:12(2625)
  31. Wang, Y.Y., Lam, Y.K. and Liu, G.R. (2001), 'A strip element method for the transient analysis of symmetric laminated plates', Int. J. Solids Struct., 38(2), 241-259 https://doi.org/10.1016/S0020-7683(00)00035-4
  32. Xue, H.Y. (1997), 'A combined finite element-Riccati transfer matrix method in frequency domain for transient structural response', Comput. Struct., 62(2), 215-220 https://doi.org/10.1016/S0045-7949(96)00192-7
  33. Yan, J.Y., Zhang, C.H. and Jin, F. (2004), 'A coupling procedure of FE and SBFE for soil-structure interaction in the time domain', Int. J. Numer. Meth. Eng., 59(11), 1453-1471 https://doi.org/10.1002/nme.923
  34. Yonemoto, A., Hisakado, T. and Okumura, K. (2003), 'Accuracy improvement of the FFT-based numerical inversion of Laplace Transforms', IEE Proceedings-Circuits Devices and Systems, 150(5), 399-404 https://doi.org/10.1049/ip-cds:20030482