Structural Engineering and Mechanics

  • 제21권1호
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  • Pages.19-33
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  • 2005
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration and elastic analysis of shear-deformable non-symmetric thin-walled curved beams: A centroid-shear center formulation

  • Kim, Nam-Il (Department of Civil and Environmental Engineering, University of Maryland) ;
  • Kim, Moon-Young (Department of Civil and Environmental Engineering, Sungkyunkwan University)
  • 투고 : 2004.09.17
  • 심사 : 2005.05.30
  • 발행 : 2005.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.

키워드

참고문헌

  1. Choi, C.K. and Hong, H.S. (2001), 'Finite strip analysis of multi-span box girder bridges by using non-periodic B-spline interpolation', Struct. Eng. Mech., 12(3), 313-328 https://doi.org/10.12989/sem.2001.12.3.313
  2. Chucheepsakul, S. and Saetiew, W. (2002), 'Free vibrations of inclined arches using finite elements', Struct. Eng. Mech., 13(6), 713-730 https://doi.org/10.12989/sem.2002.13.6.713
  3. Cortinez, V.H. and Piovan, M.T. (1999), 'Out of plane vibrations of thin-walled curved beams considering shear flexibility', Struct. Eng. Mech., 8(3), 257-272 https://doi.org/10.12989/sem.1999.8.3.257
  4. Gendy, A.S. and Saleeb, A.F. (1994), 'Vibration analysis of coupled extensional/flexural/torsional modes of curved beams with arbitrary thin-walled sections', J. Sound Vib., 174, 261-274 https://doi.org/10.1006/jsvi.1994.1275
  5. Gendy, A.S. and Saleeb, A.F. (1992), 'On the finite element analysis of the spatial response of curved beams with arbitrary thin-walled sections', Comput. Struct., 44, 639-652 https://doi.org/10.1016/0045-7949(92)90396-H
  6. Gupta, A.K. and Howson, W.P. (1994), 'Exact natural frequencies of plane structures composed of slender elastic curved members', J. Sound Vib., 175, 145-157 https://doi.org/10.1006/jsvi.1994.1319
  7. Howson, W.P. and Jemah, A.K. (1999), 'Exact out-of-plane natural frequencies of curved Timoshenko beams', J. Eng. Mech., 125, 19-25 https://doi.org/10.1061/(ASCE)0733-9399(1999)125:1(19)
  8. Kim, M.Y., Kim, N.I. and Min, B.C. (2002), 'Analytical and numerical study on spatial free vibration of nonsymmetric thin-walled curved beams', J. Sound Vib., 258(4), 595-618 https://doi.org/10.1006/jsvi.2002.5090
  9. Kim, N.I. and Kim, M.Y. (2004), 'Spatial free vibration of shear deformable circular curved beams with non-symmetric thin-walled sections', J. Sound Vib., 276, 245-271 https://doi.org/10.1016/j.jsv.2003.07.036
  10. Piovan, M.T., Cortinez, V.H. and Rossi, R.E. (2000), 'Out-of-plane vibrations of shear deformable continuous horizontally curved thin-walled beams', J. Sound Vib., 237, 101-118 https://doi.org/10.1006/jsvi.2000.3055
  11. Raveendranath, P., Singh, G. and Pradhan, B. (2000), 'Free vibration of arches using a curved beam element based on a coupled polynomial displacement field', Comput. Struct., 78, 583-590 https://doi.org/10.1016/S0045-7949(00)00038-9
  12. Saada, Adel S. (1974), Elasticity. Theory and Applications, Pergamon Press Inc.
  13. Saleeb, A.F., Chang, T.Y., Graf, W. and Yingyeunyoung, S. (1990), 'A hybrid/mixed model for nonlinear shell analysis and its applications to large-rotation problems', Int. J. Numer. Meth. Eng., 29, 407-446 https://doi.org/10.1002/nme.1620290213
  14. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability. 2nd Ed., McGraw-Hill, N.Y.
  15. Tong, G. and XU, Q. (2002), 'An exact theory for curved beams with any thin-walled open sections', Advanced in Struet. Eng., 5(4), 195-209 https://doi.org/10.1260/136943302320974572
  16. Vlasov, V.Z. (1961), Thin-walled Elastic Beams, 2nd Ed., National Science Foundation, Washington, D.C.
  17. Wilson, J.F. and Lee, B.K. (1995), 'In-plane free vibrations of catenary arches with unsymmetric axes', Struet. Eng. Mech., 3(5), 511-525 https://doi.org/10.12989/sem.1995.3.5.511
  18. Wilson, J.F., Lee, B.K. and Oh, S.J. (1994), 'Free vibrations of circular arches with variable cross-section', Struet. Eng. Mech., 2(4), 345-357 https://doi.org/10.12989/sem.1994.2.4.345

피인용 문헌

  1. Out-of-plane dynamic stability analysis of curved beams subjected to uniformly distributed radial loading vol.46, pp.11, 2011, https://doi.org/10.1007/s10778-011-0426-5