DOI QR코드

DOI QR Code

Analytical and numerical algorithm for exploring dynamic response of non-classically damped hybrid structures

  • Raheem, Shehata E. Abdel (Faculty of Engineering, Taibah University)
  • Received : 2014.04.13
  • Accepted : 2014.06.07
  • Published : 2014.06.25

Abstract

The dynamic characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of hybrid structure with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as can mass and stiffness. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. A numerical algorithm capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to explore the dynamic response of hybrid tower of cable-stayed bridges: The first approach makes use of a simplified model of 2 coupled lumped masses to investigate the effects of subsystems different damping, mass ratio, frequency ratio on dynamic characteristics and equivalent modal damping; the second approach employs a detailed numerical step-by step integration procedure.

Keywords

References

  1. Abdel Raheem, S.E. (2014), "Dynamic characteristics of hybrid tower of cable-stayed bridges", Steel Compos. Struct., (In press)
  2. Abdel Raheem, S.E. and Hayashikawa, T. (2007), "Damping characteristics in soil-foundation-superstructure interaction model of cable-stayed bridges tower", J. Construct. Steel, Japanese Soc. Steel Construct. - JSSC, 15, 261-268.
  3. Abdel Raheem, S.E. and Hayashikawa, T. (2008), "Vibration and damping characteristics of cable-stayed bridges tower", Proceedings of the International Association for Bridge and Structural Engineering - ABSE Conference, Information and Communication Technology (ICT) for Bridges, Buildings and Construction Practice, Helsinki, Finland, June 4-6, 2008, Paper ID. F15.
  4. Abdel Raheem, S.E. and Hayashikawa, T. (2013a), "Energy dissipation system for earthquake protection of cable-stayed bridge towers", Earthq. Struct., 5(6), 657-678. DOI: 10.12989/eas.2013.5.6.657
  5. Abdel Raheem, S.E. and Hayashikawa, T. (2013b), "Soil-structure interaction modeling effects on seismic response of a cable-stayed bridge tower", Adv. Struct. Eng., 5-8, 1-17. DOI: 10.1186/2008-6695-5-8
  6. Abdel Raheem, S.E., Hayashikawa, T. and Dorka, U. (2009), Seismic performance of cable-stayed bridge towers: nonlinear dynamic analysis, structural control and seismic design, VDM Verlag, ISBN: 978-3639202236.
  7. Abdel Raheem, S.E., Hayashikawa, T. and Hashimoto, I. (2003), "Effects of soil-foundation-superstructure interaction on seismic response of cable-stayed bridges tower with spread footing foundation", J. Struct. Eng. - JSCE, 49, 475-486.
  8. Adhikari, S. (2002), "Dynamics of non-viscously damped linear systems", J. Eng. Mech. - ASCE, 128(3), 328-339. DOI: 10.1061/(ASCE)0733-9399(2002)128:3(328)
  9. Adhikari, A. (2004), "Optimal complex modes and an index of damping non-proportionality", Mech. Syst. Signal Pr., 18, 1-27. DOI: 10.1016/S0888-3270(03)00048-7
  10. Angeles, J. and Ostrovskaya, S. (2002), "The proportional damping matrix of arbitrarily damped linear mechanical systems", J. Appl. Mech. - T ASME, 69, 649- 656. doi:10.1115/1.1483832
  11. Atkins, J.C. and Wilson, J.C. (2000), "Analysis of damping in earthquake response of cable-stayed bridges", Proceedings of the 12th World Conference on Earthquake Engineering, 12WCEE, Auckland, New Zealand, Paper ID 1468, 30 January - 4 February.
  12. Bert, C.W. (1973), "Material damping: an introductory review of mathematical models, measure and experimental techniques", J. Sound Vib., 29(2), 129-153. https://doi.org/10.1016/S0022-460X(73)80131-2
  13. Bread, C.F. (1979), "Damping in structural joints", J. Shock Vib. Dig., 11(9), 35 -41. https://doi.org/10.1177/058310247901100609
  14. Chang, S.Y. (2013), "Nonlinear performance of classical damping", Earthq. Eng. Eng. Vib., 12, 279-296. https://doi.org/10.1007/s11803-013-0171-3
  15. Chopra A.K. (1995), Dynamic of structures - theory and application to earthquake engineering, Prentice-Hall, Englewood Cliffs, NJ.
  16. Claret, A.M. and Venancio-Filho, F. (1991), "A modal superposition method pseudo-force method for dynamic analysis of structural systems with non-proportional damping", Earthq. Eng. Struct. Eng., 20, 303-315. DOI: 10.1002/eqe.4290200402
  17. Clough, R.W. and Mojtadhedi, S. (1976), "Earthquake response analysis considering non-proportional damping", Earthq. Eng. Struct. D., 4(5), 489-496. DOI: 10.1002/eqe.4290040506
  18. Corte´s, F. and Elejabarrieta, M.J. (2006), "Computational methods for complex eigen problems in finite element analysis of structural systems with viscoelastic damping treatments", Comput. Method. Appl. M., 195, 6448-6462. DOI: 10.1016/j.cma.2006.01.006.
  19. Ding, N.H., Lin, L.X. and Chen, J.D. (2011), "Seismic response analysis of double chains suspension bridge considering non-classical damping", Adv. Mater. Res., 255-260, 826-830. DOI: 10.4028/AMR.255-260.826
  20. Du, Y., Li, H. and Spencer, Jr B.F. (2002), "Effect of non-proportional damping on seismic isolation", J. Struct. Control, 9, 205-236. DOI: 10.1002/stc.13
  21. Falsone, G. and Muscolino, G. (2004), "New real-value modal combination rules for non-classically damped structures", Earthq. Eng. Struct. Eng., 33, 1187-1209. DOI: 10.1002/eqe.394
  22. Ganev, T., Yamazaki, F. and Katayama, T. (1995), "Observation and numerical analysis of soil-structure interaction of reinforced concrete tower", Earthq. Eng. Struct. D., 24(4), 491-503. https://doi.org/10.1002/eqe.4290240403
  23. Harada, T., Kubo, K. and Katayama, T. (1981), Dynamic soil-structure interaction analysis by continuum formulation method, Report of the Institute of Industrial Science, University of Tokyo, 29(5),139-194.
  24. Hayashikawa, T., Abdel Raheem, S.E. and Hashimoto, I. (2004), "Nonlinear seismic response of soil-foundation-structure interaction model of cable-stayed bridges tower", Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada, 1-6 August, Paper No. 3045.
  25. Huang, B.C., Leung, A.Y.T., Lam, K.M. and Cheung Y.K. (1995), "Analytical determination of equivalent modal damping ratios of a composite tower in wind-induced vibrations", Comput. Struct., 59(2), 311-316. DOI: 10.1016/0045-7949(95)00258-8
  26. Ibrahimbegovic, A. and Wilson, E.L. (1989), "Simple numerical algorithms for the mode superposition analysis of linear structural systems with non-proportional damping", Comput. Struct., 33(2), 523-531. DOI: 10.1016/0045-7949(89)90026-6
  27. Ibrahimbegovic, A., Chen, H.C., Wilson, E.L. and Taylor, R.L. (1990), "Ritz method for dynamic analysis of large discrete linear systems with non-proportional damping", Earthq. Eng. Struct. D., 19(6), 877-889. DOI: 10.1002/eqe.4290190608
  28. Igusa, T., Der Kiureghian, A. and Sackman, J.L. (1984), "Modal decomposition method for stationary response of non-classically damped systems", Earthq. Eng. Struct. D., 12(1), 121-136. DOI: 10.1002/eqe.4290120109
  29. Japan Road Association (1996), Reference for highway bridge design, specification for highway bridges-part IV substructures, Chapter 7-9.
  30. Japan Road Association (2002), Specification for highway bridges-Part V Seismic design, Maruzen, Tokyo, Japan.
  31. Jehel, P., Leger, P. and Ibrahimbegovic, A. (2014), "Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses", Earthq. Eng. Struct. D., 43(3), 467-484. https://doi.org/10.1002/eqe.2357
  32. Johnson, C.D. and Kienhholz, D.A. (1982), "Finite element prediction of damping in structures", Am. Inst. Aeronaut. Astronaut. J., 20(9), 1284-1290. https://doi.org/10.2514/3.51190
  33. Kawashima, K., Unjoh, S. and Tunomoto, M. (1993), "Estimation of damping ratio of cable-stayed bridges for seismic design", J. Struct. Eng. - ASCE, 119(4), 1015-1031. DOI: 10.1061/(ASCE)0733-9445(1993)119:4(1015)
  34. Khanlari, K. and Ghafory-Ashtiany, M. (2005), "New approaches for non-classically damped system Eigen analysis", Earthq. Eng. Struct. Eng., 34, 1073-1087. DOI: 10.1002/eqe.467
  35. Kusainov, A.A. and Clough, R.W. (1988), Alternatives to standard mode superposition for analysis of non-classically damped systems, UCB/EERC-88/09, University of California at Berkeley, CA.
  36. Lee, S.H., Min, K.W., Hwang, J.S. and Kim, J. (2004), "Evaluation of equivalent damping ratio of a structure with added dampers", Eng. Struct., 26, 335-346. DOI: 10.1016/j.engstruct.2003.09.014
  37. Ma, F. and Morzfeld, M. (2011), "A general methodology for decoupling damped linear systems", Proceedings of the 12th East Asia-Pacific Conference on Structural Engineering and Construction - EASEC12, Procedia Engineering, 14, 2498-2502. DOI: 10.1016/j.proeng.2011.07.314
  38. Papageorgiou, A.V. and Gantes C.J. (2010), "Equivalent modal damping ratios for concrete/steel mixed structures", Comput. Struct., 88 (19-20), 1124-1136. DOI: 10.1016/j.compstruc.2010.06.014
  39. Papageorgiou, A.V. and Gantes C.J. (2011), "Equivalent uniform damping ratios for linear irregularly damped concrete/steel mixed structures", Soil Dyn. Earthq. Eng., 31(3), 418-430. DOI: 10.1016/j.soildyn.2010.09.010
  40. Park, D. and Hashash, Y.M.A. (2004), "Soil damping formulation in nonlinear time domain site response analysis", J. Earthq. Eng., 8(2), 249-274. DOI: 10.1080/13632460409350489
  41. Perotti, F. (1994), "Analytical and numerical techniques for the dynamic analysis of non-classically damped linear systems", Soil Dyn. Earthq. Eng., 13,197-212. DOI: 10.1016/0267-7261(94)90018-3
  42. Petrini, L., Maggi, C., Priestley, M.J.N. and Calvi, G.M. (2008), "Experimental verification of viscous damping modelling for inelastic time history analyses", J. Earthq. Eng., 12(1), 125-145. DOI:10.1080/13632460801925822
  43. Prater, G. and Singh, R. (1990), "Eigenproblem formulation, solution and interpretation for non-proportionally damped continuous beams", J. Sound Vib., 143(1), 125-142. DOI: 10.1016/0022-460X (90)90572-H
  44. Prells, U. and Friswell, M.I. (2000), "A measure of non-proportional damping", Mech. Syst. Signal Pr., 14(2), 125-137. DOI: 10.1006/mssp.1999.1280
  45. Qin, Q. and Lou, L. (2000), "Effects of non proportional damping on the seismic responses of suspension bridges", Proceedings of the 12th world conference of earthquake Engineering, Auckland, New Zealand, 30 January - 4 February 2000, paper No. 0529.
  46. Qu, Z.Q., Selvam, R.P. and Jung, Y. (2003), "Model condensation for non-classically damped systems-part ii: iterative schemes for dynamic condensation", Mech. Syst. Signal Pr., 17(5), 1017-1032. DOI:10.1006/mssp.2002.1527
  47. Raggett, J.D. (1975), "Estimation of damping of real structures," J. Struct. Division -ASCE, 101(9), 1823-1835.
  48. Roesset, J.M., Whitman, R.V. and Dobry, R. (1973), "Modal analysis for structures with foundation interaction", J. Struct. Division - ASCE, 99, 399-415.
  49. Veletsos, A.S. and Ventura, C.E. (1986), "Model analysis of non-classically damped linear systems", Earthq. Eng. Struct. D., 14, 217-243. DOI: 10.1002/eqe.4290140205
  50. Villaverde, R. (2008), "A complex modal superposition method for the seismic analysis of structures with supplemental dampers", Proceedings of the 14th World Conference on Earthquake Engineering, 14WCEE, Beijing, China.
  51. Wagner, N. and Adhikari, S. (2003), "Symmetric state-space formulation for a class of non-viscously damped systems", The American Institute of Aeronautics and Astronautics, AIAA J., 41(5), 951-956. https://doi.org/10.2514/2.2032
  52. Warburton, G.B. and Soni, S.R. (1977), "Errors in response calculations for non-classically damped structures", Earthq. Eng. Struct. D., 5(4), 365-376. DOI: 10.1002/eqe.4290050404
  53. Xu, J., DeGrassi, G. and Chokshi, N. (2004a), "A NRC-BNL benchmark evaluation of seismic analysis methods for non-classically damped coupled systems", Nucl. Eng. Des., 228, 345-366. DOI:10.1016/j.nucengdes.2003.06.019.
  54. Xu, J., DeGrassi, G. and Chokshi, N. (2004b), "Insights Gleaned from NRC-BNL benchmark evaluation of seismic analysis methods for non-classically damped coupled systems", J. Pressure Vessel Technol., 126, 75 -84. DOI:10.1115/1.1638388.

Cited by

  1. Frequency analysis of beams with multiple dampers via exact generalized functions vol.5, pp.2, 2016, https://doi.org/10.12989/csm.2016.5.2.157
  2. A simplified seismic design approach for mid-rise buildings with vertical combination of framing systems vol.99, 2015, https://doi.org/10.1016/j.engstruct.2015.05.019