Acceleration Transfer Function of Secondary Systems

Vinay K. Gupta

Assoc. Prof., Dept. of Civ. Engrg., Indian Inst. of Technol., Kanpur-208016, India.

This paper presents an alternative formulation for the transfer function of the absolute acceleration response of a single-degree-of-freedom (SDOF) secondary system supported on an earthquake-excited, classically damped primary system. This formulation is based on the use of fixed-base mode shapes of the primary system and thus does not require the computation of the modal properties of the combined system. This formulation requires the knowledge of the power-spectral-density function of the earthquake motion to obtain the desired floor response spectra. This has been illustrated in the case of an example building and a band-limited white noise excitation.

References

  1. Borino, G., and Muscolino, G.(1986). "Mode-superposition methods in dynamic analysis of classically and non-classically damped linear systems."Earthquake Engrg. and Struct. Dyn., 14, 705–717.
  2. Chen, G., and Soong, T. T.(1994). "Energy-based dynamic analysis of secondary systems."J. Engrg. Mech., ASCE, 120(3), 514–534.
  3. Chopra, A. K., and Gutierrez, J. A.(1974). "Earthquake response analysis of multistorey buildings including foundation interaction."Earthquake Engrg. and Struct. Dyn., 3, 65–77.
  4. Crandall, S. H., and Mark, W. D. (1963). Random vibration in mechanical systems. Academic Press, Inc., New York, N.Y.
  5. Der Kiureghian, A., and Nakamura, Y.(1993). "CQC modal combination rule for high-frequency modes."Earthquake Engrg. and Struct. Dyn., 22, 943–956.
  6. Foss, K. A. (1958). "Coordinates which uncouple the equations of motion of damped linear dynamic systems."J. Appl. Mech., 25(E), 361–364.
  7. Gupta, I. D., and Joshi, R. G.(1993). "On synthesizing response spectrum compatible accelerograms."Eur. Earthquake Engrg., Bologna, Italy, 7(2), 25–33.
  8. Gupta, I. D., and Trifunac, M. D.(1990). "Probabilistic spectrum superposition for response analysis including the effects of soil-structure interaction."J. Probabilistic Engrg. Mech., 5(1), 9–18.
  9. Gupta, V. K., and Trifunac, M. D.(1991). "Seismic response of multistoried buildings including the effects of soil-structure interaction."Soil Dyn. and Earthquake Engrg., 10(8), 414–422.
  10. Igusa, T., and Der Kiureghian, A.(1985). "Generation of floor response spectra including oscillator-structure interaction."Earthquake Engrg. and Struct. Dyn., 13, 661–676.
  11. Igusa, T., Der Kiureghian, A., and Sackman, J. L.(1984). "Modal decomposition method for stationary response of non-classically damped systems."Earthquake Engrg. and Struct. Dyn., 12, 121–136.
  12. Itoh, T.(1973). "Damped vibration mode superposition method for dynamic response analysis."Earthquake Engrg. and Struct. Dyn., 2, 47–57.
  13. Kanai, K.(1957). "Semi-empirical formula for the seismic characteristics of the ground."Bull. Earthquake Res. Inst., Tokyo, Japan, 35, 309–325.
  14. Kaul, M. K.(1978). "Stochastic characterization of earthquake through their response spectrum."Earthquake Engrg. and Struct. Dyn., 6, 497–509.
  15. Mau, S. T.(1988). "A subspace modal superposition method for non-classically damped systems."Earthquake Engrg. and Struct. Dyn., 16, 931–942.
  16. Perotti, F.(1994). "Analytical and numerical techniques for the dynamic analysis of non-classically damped linear systems."Soil Dyn. Earthquake Engrg., 13, 197–212.
  17. Sackman, J. L., Der Kiureghian, A., and Nour-Omid, B.(1983). "Dynamic analysis of light equipment in structures: modal properties of the combined system."J. Engrg. Mech., ASCE, 109(1), 73–110.
  18. Sackman, J. L., and Kelly, J. M.(1979). "Seismic analysis of internal equipment and components in structures."Engrg. Struct., 1(4), 179–190.
  19. Singh, M. P.(1975). "Generation of seismic floor spectra."J. Engrg. Mech. Div., ASCE, 101(5), 593–607.
  20. Singh, M. P.(1980a). "Seismic design input for secondary systems."J. Engrg. Mech. Div., ASCE, 106(2), 505–517.
  21. Singh, M. P.(1980b). "Seismic response by SRSS for nonproportional damping."J. Engrg. Mech. Div., ASCE, 106(6), 1405–1419.
  22. Singh, M. P., and Mehta, K. B.(1983). "Seismic design response by an alternative SRSS rule."Earthquake Engrg. and Struct. Dyn., 11, 771–783.
  23. Singh, M. P., and Suarez, L. E.(1987). "Seismic response analysis of structure-equipment systems with non-classical damping effects."Earthquake Engrg. and Struct. Dyn., 15, 871–888.
  24. Suarez, L. E., and Singh, M. P. (1987a). "Seismic response of SDF equipment-structure system."J. Engrg. Mech., ASCE, 113(1), 16– 30.
  25. Suarez, L. E., and Singh, M. P.(1987b). "Floor response spectra with structure-equipment interaction effects by a mode synthesis approach."Earthquake Engrg. and Struct. Dyn., 15, 141–158.
  26. Tajimi, H. (1960). "A standard method of determining the maximum response of a building structure during an earthquake."Proc., 2nd World Conf. on Earthquake Engrg., Tokyo, Japan, Science Council of Japan, 781–797.
  27. Traill-Nash, R. W.(1981). "Modal methods in the dynamics of systems with non-classical damping."Earthquake Engrg. and Struct. Dyn., 9, 153–169.
  28. Unruh, J. F., and Kana, D. D.(1981). "An iterative procedure for the generation of consistent power/response spectrum."Nuclear Engrg. Des., 66, 427–435.
  29. Veletsos, A. S., and Ventura, C. E.(1986). "Modal analysis of non-classically damped linear systems."Earthquake Engrg. and Struct. Dyn., 14, 217–243.
  30. Wu, W.-H., and Smith, H. A.(1995). "Efficient modal analysis for structures with soil-structure interaction."Earthquake Engrg. and Struct. Dyn., 24, 283–299.