DOI QR코드

DOI QR Code

Dynamic stiffness formulations for harmonic response of infilled frames

  • Bozyigit, Baran (Department of Civil Engineering, Dokuz Eylul University) ;
  • Yesilcea, Yusuf (Department of Civil Engineering, Dokuz Eylul University)
  • 투고 : 2018.05.01
  • 심사 : 2018.08.17
  • 발행 : 2018.10.25

초록

In this paper, harmonic responses of infilled multi-storey frames are obtained by using a single variable shear deformation theory (SVSDT) and dynamic stiffness formulations. Two different planar frame models are used which are fully infilled and soft storey. The infill walls are modeled by using equivalent diagonal strut approach. Firstly, free vibration analyses of bare frame and infilled frames are performed. The calculated natural frequencies are tabulated with finite element solution results. Then, harmonic response curves (HRCs) of frame models are plotted for different infill wall thickness values. All of the results are presented comparatively with Timoshenko beam theory results to reveal the effectiveness of SVSDT which considers the parabolic shear stress distribution along the frame member cross-sections.

키워드

참고문헌

  1. Abdelbari, S., Amar, L.H.H., Kaci, A. and Tounsi, A. (2018), "Single variable shear deformation model for bending analysis of thick beams", Struct. Eng. Mech., 67(3), 291-300. https://doi.org/10.12989/SEM.2018.67.3.291
  2. Ai, Z.H. and Ren, G.P. (2017), "Dynamic response of an infinite beam on a transversely isotropic multilayered half-space due to a moving load", Int. J. Mech. Sci., 133, 817-828. https://doi.org/10.1016/j.ijmecsci.2017.09.042
  3. Al-Balhawi, A. and Zhang, B. (2017), "Investigations of elastic vibration periods of reinforced concrete moment-resisting frame systems with various infill walls", Eng. Struct., 151, 173-187. https://doi.org/10.1016/j.engstruct.2017.08.016
  4. Attar, M., Karrech, A. and Regenauer-Lieb, K. (2017), "Dynamic response of cracked Timoshenko beams on elastic foundations under moving harmonic loads", J. Vibr. Contr., 23(3), 432-457. https://doi.org/10.1177/1077546315580470
  5. Banerjee, J.R. (1997), "Dynamic stiffness for structural elements: A general approach", Comput. Struct., 63(1), 101-103. https://doi.org/10.1016/S0045-7949(96)00326-4
  6. Banerjee, J.R. and Ananthapuvirajah, A. (2018), "Free vibration of functionally graded beams and frameworks using the dynamic stiffness method", J. Sound Vibr., 422, 34-47. https://doi.org/10.1016/j.jsv.2018.02.010
  7. Banerjee, J.R. and Jackson, D.R. (2013), "Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution", Comput. Struct., 124, 11-20. https://doi.org/10.1016/j.compstruc.2012.11.010
  8. Beiraghi, H. (2016), "Fundamental period of masonry infilled moment-resisting frame buildings", Struct. Des. Tall Spec., 26(5), 1-10.
  9. Bickford, W.B. (1982), "A consistent higher order beam theory", Develop. Theoret. Appl. Mech., 11, 137-150.
  10. Bozyigit, B. and Yesilce, Y. (2016), "Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam", Struct. Eng. Mech., 58(5), 847-868. https://doi.org/10.12989/sem.2016.58.5.847
  11. Bozyigit, B. and Yesilce, Y. (2018) "Investigation of natural frequencies of multi-bay and multi-storey frames using single a variable shear deformation theory", Struct. Eng. Mech., 65(1), 9-17. https://doi.org/10.12989/SEM.2018.65.1.009
  12. Chaker, A.A. and Cherifati, A. (1999), "Influence of masonary infill panels on the vibration and stiffness characteristics of R/C frame building", Earthq. Eng. Struct. Dyn., 28, 1061-1065. https://doi.org/10.1002/(SICI)1096-9845(199909)28:9<1061::AID-EQE856>3.0.CO;2-3
  13. Damanpack, A.R. and Khalili, S.M.R. (2012), "High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method", Compos. Struct., 94(5), 1503-1514. https://doi.org/10.1016/j.compstruct.2011.08.023
  14. Deng, H., Chen, K., Cheng, W. and Zhao, S. (2017), "Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternac elastic foundation", Compos. Struct., 160, 152-168. https://doi.org/10.1016/j.compstruct.2016.10.027
  15. Dilena, M. and Morassi, A. (2004), "The use of antiresonances for crack detection in beams", J. Sound Vibr., 276, 195-214. https://doi.org/10.1016/j.jsv.2003.07.021
  16. El-Dakhakhni W.W., Elgaaly, M. and Hamid, A.A. (2003), "Threestrut model for concrete masonary-infilled steel frames", J. Struct. Eng., 129(2), 177-185. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(177)
  17. Eurocode 6 (1996), Design of Masonry Structures-Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures, European Committee for Standardization, Brussels, Belgium.
  18. FEMA-356 (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, U.S.A.
  19. Ghandi, E. and Shiri, B. (2017), "On triply coupled vibration of eccentrically loaded thin-walled beam using dynamic stiffness matrix method", Struct. Eng. Mech., 62(6), 759-769. https://doi.org/10.12989/SEM.2017.62.6.759
  20. Ghandi, E., Rafezy, B. and Howson, W.P. (2012), "On the biplanar motion of a Timoshenko beam with shear resistant infill", Int. J. Mech. Sci., 57(1), 1-8. https://doi.org/10.1016/j.ijmecsci.2011.12.011
  21. Ghugal, Y.M. and Shimpi, R.P. (2001), "A review of refined shear deformation theories for isotropic laminated beams", J. Reinf. Plast. Comp., 20(3), 255-272. https://doi.org/10.1177/073168401772678283
  22. Grossi, R.O. and Albarracin, C.M. (2013), "Variational approach to vibrations of frames with inclined members", Appl. Acoust., 74(3), 325-334. https://doi.org/10.1016/j.apacoust.2012.07.014
  23. Han, F., Dan, D. and Cheng, W. (2018), "An exact solution for dynamic analysis of a complex double-beam system", Compos. Struct., 193, 295-305. https://doi.org/10.1016/j.compstruct.2018.03.088
  24. Han, H., Cao, D. and Liu, L. (2017), "Green's functions for forced vibration analysis of bending-torsion coupled Timoshenko beam", Appl. Math. Model., 45, 621-635. https://doi.org/10.1016/j.apm.2017.01.014
  25. Han, S.M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vibr., 225(5), 936-988.
  26. Hanson, D, Waters, T.P., Thompson, D.J., Randall, R.B. and Ford, R.A.J. (2007), "The role of anti-resonance frequencies from operational modal analysis in finite element model updating", Mech. Syst. Sign. Pr., 21(1), 74-97. https://doi.org/10.1016/j.ymssp.2006.01.001
  27. Heyliger, P.R. and Reddy, J.N. (1988), "A higher order beam finite element for bending and vibration problems", J. Sound Vibr., 126(2), 309-326. https://doi.org/10.1016/0022-460X(88)90244-1
  28. Holmes, M. (1961), "Steel Frames with brick work and concrete infilling", Proceedings of the Institution of the Civil Engineers, 19(4), 473-478. https://doi.org/10.1680/iicep.1961.11305
  29. Holmes, M. (1963), "Combined loading on infilled frames", Proceeding of the Institution of Civil Engineers, 25(1), 31-38. https://doi.org/10.1680/iicep.1963.10685
  30. Howson, W.P. and Watson, A. (2017), "Exact eigensolution of a class of multi-level elastically connected members", Eng. Struct., 143, 375-383. https://doi.org/10.1016/j.engstruct.2017.03.059
  31. Jones, K. and Turcotte, J. (2002), "Finite element model updating using antiresonant frequencies", J. Sound Vibr., 252(4), 717-727. https://doi.org/10.1006/jsvi.2001.3697
  32. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., 63(4), 439-446. https://doi.org/10.12989/SEM.2017.63.4.439
  33. Labib, A., Kennedy, D. and Featherstone, C. (2014), "Free vibration analysis of beams and frames with multiple cracks for damage detection", J. Sound Vibr., 333(20), 4991-5003. https://doi.org/10.1016/j.jsv.2014.05.015
  34. Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vibr., 74(1), 81-87. https://doi.org/10.1016/0022-460X(81)90493-4
  35. Li, H., Yin, X. and Wu, W. (2016), "Dynamic stiffness formulation for in-plane and bending vibrations of plates with two opposite edges simply supported", J. Vibr. Contr., 24(9), 1652-1669. https://doi.org/10.1177/1077546316667205
  36. Lien, N. and Yao, G.C. (2000), "Identification of anti-resonance frequency in buildings based on vibration measurements", Proceedings of the 12th World Conference on Earthquake Engineering, Auckland.
  37. Mainstone, R.J. (1974), Supplementary Note on the Stiffness and Strenght of Infilled Frames, Building Research Establishment, London, U.K.
  38. Mei, C. (2012), "Free vibration analysis of classical single-storey multi-bay planar frames", J. Vibr. Contr., 19(13), 2022-2035. https://doi.org/10.1177/1077546312455081
  39. Mei, C. (2018), "Analysis of in- and out-of plane vibrations in a rectangular frame based on two- and three dimensional structural models", J. Sound Vibr., 1-28.
  40. Mei, C. and Sha, H. (2015), "Analytical and experimental study of vibrations in simple spatial structures", J. Vibr. Contr., 22(17), 3711-3735. https://doi.org/10.1177/1077546314565807
  41. Miao, Y., Shi, Y., Luo, H. and Gao, R. (2018), "Closed-form solution considering the tangential effect under harmonic line load for an infinite Euler-Bernoulli beam on elastic foundation", Appl. Math. Model., 54, 21-33. https://doi.org/10.1016/j.apm.2017.09.040
  42. Naprstek, J. and Fischer, C. (2017), "Investigation of bar system modal characteristics using dynamic stiffness matrix polynomial approximations", Comput. Struct., 180, 3-12. https://doi.org/10.1016/j.compstruc.2016.10.015
  43. Ozturkoglu, O., Ucar, T. and Yesilce, Y. (2017), "Effect of masonary infill walls with openings on nonlinear response of reinforced concrete frames", Earthq. Struct., 12(3), 333-347. https://doi.org/10.12989/eas.2017.12.3.333
  44. Paz, M. and Leigh, W. (2004), Structural Dynamics-Theory and Computation, Kluwer Academic Publishers, U.S.A.
  45. Polyakov, S.V. (1950), Investigation of the Strength and of the Deformational Characteristics of Masonry Filler Walls and facing on Framed Structures, Construction Industry Institute 3.
  46. Rao, S.S. (1995), Mechanical Vibrations, Addison-Wesley Publishing Company, U.S.A.
  47. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  48. Rubio, L., Fernandez-Saez, J. and Morassi, A. (2015), "Identification of two cracks in a rod by minimal resonant and antiresonant frequency data", Mech. Syst. Sign. Pr., 60, 1-13.
  49. Salama, M.I. (2015), "Estimation of period of vibration for concrete moment-resisting frame buildings", Hous. Build. Nat. Res. Center, 11(1), 16-21.
  50. Shimpi, R.P, Patel, H.G. and Arya, H. (2007), "New first order shear deformation plate theories", J. Appl. Mech., 74(3), 523-533. https://doi.org/10.1115/1.2423036
  51. Shimpi, R.P, Shetty, R.A. and Guha, A. (2017), "A simple single variable shear deformation theory for a rectangular beam", J. Mech. Eng. Sci., 231(24), 4576-4591. https://doi.org/10.1177/0954406216670682
  52. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622
  53. Su, H. and Banerjee, J.R. (2015), "Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams", Comput. Struct., 147, 107-116. https://doi.org/10.1016/j.compstruc.2014.10.001
  54. Tamboli, H.R. and Karadi, U.N. (2012), "Seismic analysis of RC frame structure with and without masonary infill walls", Ind. J. Nat. Sci., 3(14), 1137-1194.
  55. Tan, G., Wang, W., Cheng, Y., Wei, H., Wei, Z. and Li, H. (2018), "Dynamic response of a nonuniform Timoshenko beam with elastic supports, subjected to a moving spring-mass system", Int. J. Struct. Stab. Dyn., 18(5), 1850066-1-1852266-23. https://doi.org/10.1142/S0219455418500669
  56. Thambiratnam, D. (2009), "Modelling and analysis of infilled frame structures under seismic loads", Open Constr. Build. Technol. J., 3, 119-126. https://doi.org/10.2174/1874836800903010119
  57. Thinh, T.I. and Nguyen, M.C. (2016), "Dynamic stiffness matrix of continuous element for vibration of thick cross-ply laminated composite cylindrical shells", Compos. Struct., 98, 93-102.
  58. Tounsi, D., Casimir, J.B., Abid, S., Tawfiq, I. and Haddar, M. (2014), "Dynamic stiffness formulation and response analysis of stiffened shells", Comput. Struct., 132, 75-83. https://doi.org/10.1016/j.compstruc.2013.11.003
  59. Zhang, C., Jin, G., Ye, T. and Zhang, Y. (2018), "Harmonic response analysis of coupled plate structures using the dynamic stiffness method", Thin Wall Struct., 127, 402-415. https://doi.org/10.1016/j.tws.2018.02.014

피인용 문헌

  1. Coupled‐two‐beam discrete model for dynamic analysis of tall buildings with tuned mass dampers including soil–structure interaction vol.29, pp.1, 2018, https://doi.org/10.1002/tal.1683