DOI QR코드

DOI QR Code

Free vibration analysis of combined system with variable cross section in tall buildings

  • 투고 : 2011.09.08
  • 심사 : 2012.05.01
  • 발행 : 2012.06.10

초록

This paper deals with determining the fundamental frequency of tall buildings that consist of framed tube, shear core, belt truss and outrigger systems in which the framed tube and shear core vary in size along the height of the structure. The effect of belt truss and outrigger system is modeled as a concentrated rotational linear spring at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilevered beams with variable cross-section in free vibration analysis. In this paper, the continuous approach, in which a tall building is replaced by an idealized cantilever continuum representing the structural characteristics, is employed and by using energy method and Hamilton's variational principle, the governing equation for free vibration of tall building with variable distributed mass and stiffness is obtained. The general solution of governing equation is obtained by making appropriate selection for mass and stiffness distribution functions. By applying the separation of variables method for time and space, the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients with the assumption that the transverse displacement is harmonic. A power-series solution representing the mode shape function of tall building is used. Applying boundary conditions yields the boundary value problem; the frequency equation is established and solved through a numerical process to determine the natural frequencies. Computer program has been developed in Matlab (R2009b, Version 7.9.0.529, Mathworks Inc., California, USA). A numerical example has been solved to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure's dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages.

키워드

참고문헌

  1. Bozdogan, K.B. (2006), "A method for free vibration analysis of stiffened multi-bay coupled shear walls", Asian J. Civil Eng., 6, 639-649.
  2. Bozdogan, K.B. (2009), "An approximate method for static and dynamic analysis of symmetric wall-frame buildings", Struct. Des. Tall Spec. Build., 18, 279-290. https://doi.org/10.1002/tal.409
  3. Connor, J.J. and Pouangare, C.C. (1991), "Simple model for design of framed tube structures", J. Struct. Eng.- ASCE, 117, 3623-3644. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:12(3623)
  4. Coull, A. and Bose, B. (1975), "Simplified analysis of frame tube structures", J. Struct. Div., 101, 2223-2240.
  5. Coull, A. and Ahmed, K. (1978), "Deflection of framed-tube structures", J. Struct. Div., 104, 857-862.
  6. Eisenberger, M. (1991a), "Exact solution for general variable cross-section members", J. Comput. Struct., 4, 765-772.
  7. Eisenberger, M. (1991b), "Exact longitudinal vibration frequencies of a variable cross-section rod", J. Appl. Acoust., 34, 123-130. https://doi.org/10.1016/0003-682X(91)90027-C
  8. Eisenberger, M. (1994), "Vibration frequencies for beams on variable one and two parameter elastic foundations", J. Sound Vib., 175, 577-584. https://doi.org/10.1006/jsvi.1994.1347
  9. Hoenderkamp, J.C.D. and Bakker, M.C.M. (2003), "Analysis of high-rise braced frames with outriggers", Struct. Des. Tall Spec. Build., 12, 335-350. https://doi.org/10.1002/tal.226
  10. Kaviani, P., Rahgozar, R. and Saffari, H. (2008), "Approximate analysis of tall buildings using sandwich beam models with variable cross-section", Struct. Des. Tall Spec. Build., 17, 401-418. https://doi.org/10.1002/tal.360
  11. Kuang, J.S. and Ng, S.C. (2004), "Coupled vibration of tall buildings structures", Struct. Des. Tall Spec. Build., 13, 291-303. https://doi.org/10.1002/tal.253
  12. Kuang, J.S. and Ng, S.C. (2009), "Lateral shear St. Venant torsion coupled vibration of asymmetric-plan frame structures", Struct. Des. Tall Spec. Build., 18, 647-656. https://doi.org/10.1002/tal.456
  13. Kwan, A.K.H. (1994), "Simple method for approximate analysis of framed tube structures", J. Struct. Eng.- ASCE, 120, 1221-1239. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1221)
  14. Lee, W.H. (2007), "Free vibration analysis for tube-in-tube tall buildings", J. Sound Vib., 303, 287-304. https://doi.org/10.1016/j.jsv.2007.01.023
  15. Lee, J., Bang, M. and Kim, J.Y. (2008), "An Analytical model for high-rise wall-frame structures with outriggers", Struct. Des. Tall Spec. Build., 17, 839-851. https://doi.org/10.1002/tal.406
  16. Li, Q.S., Fang, J.Q. and Jeary, A.P. (2000), "Free vibration analysis of cantilevered tall structures under various axial loads", J. Eng. Struct., 22, 525-534. https://doi.org/10.1016/S0141-0296(98)00124-2
  17. Malekinejad, M. and Rahgozar R., (2011), "Free Vibration analysis of tall buildings with outrigger-belt truss system", Int. J. Earthq. Struct., 2(1), 89-107. https://doi.org/10.12989/eas.2011.2.1.089
  18. Piersol, A.G. and Paez, T.L. (2010), Harri's Shock and Vibration Handbook, McGraw-Hill, New York.
  19. Rahgozar, R. and Sharifi, Y. (2009), "An approximate analysis of combined system of framed tube, shear core and belt truss in high-rise buildings", Struct. Des. Tall Spec. Build., 18(6), 607-624. https://doi.org/10.1002/tal.503
  20. Rahgozar, R., Ahmadi, A.R, Hosseini, O. and Malekinejad, M. (2011) "A simple mathematical model for static analysis of tall buildings with two outrigger-belt truss systems", Struct. Eng. Mech., 40(1), 65-84. https://doi.org/10.12989/sem.2011.40.1.065
  21. Rutenberg, A. and Tal, D. (1987), "Lateral load response of belted tall building structures", J. Eng. Struct., 9, 53-67. https://doi.org/10.1016/0141-0296(87)90041-1
  22. Stafford Smith, B. and Salim, I. (1983), "Formulae for optimum drift resistance of outrigger braced tall building structures", J. Comput. Struct., 17, 45-50. https://doi.org/10.1016/0045-7949(83)90027-5
  23. Stafford Smith, B. and Coull, A. (1991), Tall Building Structures, Analysis and Design, Wiley, New York.
  24. Swaddiwudhipong, S., Soelarno Sidji, S. and Lee, S.L. (2002), "The effects of axial deformation and axial force on vibration characteristics of tall buildings", Struct. Des. Tall Spec. Build., 11, 309-328. https://doi.org/10.1002/tal.203
  25. Taranath, B.S. (1988), Structural Analysis and Design of Tall Buildings, McGraw-Hill, New York.
  26. Tuma, J.J. and Cheng, F.Y. (1983), Dynamic Structural Analysis, McGraw-Hill, New York.
  27. Wang, G.Y. (1978), Vibration of Building and Structures, Science and Technology Press, Beijing.
  28. Wang, Q. (1996a), "Sturm-Liouville equation for free vibration of a tube-in-tube tall building", J. Sound Vib., 191, 349-355. https://doi.org/10.1006/jsvi.1996.0126
  29. Wang, Q. (1996b), "Modified ODE-solver for vibration of tube-in-tube structures", Comput. Meth. Appl. Mech. Eng., 129, 151-156. https://doi.org/10.1016/0045-7825(95)00895-0

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