Coupled Flexural-Torsional Vibrations of Timoshenko Beams of Monosymmetric Cross-Section including Warping

워핑을 고려한 일축 대칭단면을 갖는 Timoshenko보의 휨-비틀림 연성진동

  • 이병구 (원광대학교 공과대학 토목환경공학과) ;
  • 오상진 (담양대학 토목과) ;
  • 진태기 (원광대학교 대학원 토목환경공학과) ;
  • 이종국 (원광대학교 대학원 토목환경공학과)
  • Published : 1999.10.01

Abstract

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

Keywords

References

  1. Journal of Sound and Vibration v.119 An Exact Solution for Coupled Band Torsion Vibrations of Uniform Beams Having Single Cross-sectional Symmetry Documaci, E.
  2. International Journal for Numerical Methods in Engineering v.28 Coupled Bending-Torsional Dynamic Stiffness Matrix for Beam Elements Banerjee, J. R.
  3. Journal of Sound and Vibration v.131 On Coupled Bending and Torsional Vibration of Uniform Beams Bishop, R. E. D.;Cannon, S. M.;Miao, S.
  4. Journal of Sound and Vibration v.183 Theoretical and Experimental Study of Coupled Vibration Klausbruckner, M. J.;Pryputniewicz, R. J.
  5. Computers and Structures v.59 Exact Dynamic Stiffness Matrix of a Bending-Torsion Coupled Beam Including Warping Banerjee, J. R.;Guo, S.;Howson, W. P.
  6. International Journal for Numerical Methods in Engineering v.21 Beam Element Matrices Derived from Vlasov's Theory of Open thin-Walled Elastic Beams Friberg, P. O.
  7. Thin Walled Structures v.11 Natural Shape Functions of Compressed Vlasov Element Leung, A. Y. T.
  8. Thin Walled Structures v.14 Dynamic Stiffness Analysis of Thin-Walled Structures Leung, A. Y. T.
  9. 한국소음진동공학회지 v.5 no.3 휨과 비틀림이 연계된 채널보의 진동 김상환
  10. Journal of Sound and Vibration v.50 Couple Bending and Twisting of a Timoshenko Beam Bishop, R. E. D.;Price, W. G.
  11. Journal of Sound and Vibration v.99 A Note on the Dynamical Behaviour of Uniform Beams Having Open Channel Section Bushop, R. E. D.;Price, W. G.Zhang, X. C.
  12. Computers and Structures v.42 Coupled Flexural-Torsional Dynamic Stiffness Matrix for Timoshenko Beam Elements Banerjee, J. R.;Williams, F. W.
  13. Journal of Sound and Vibration v.207 Coupled Flexual-Torsional Vibrations of Timoshenko Beams Bercin, A. N.;Tanaka, M.
  14. Bending and Torsional Design in Structural Members Heins, C. P.
  15. Vibration Problems in Engineering Timoshenko, s. P.;Young, D. H.;Weaver, Jr. W.
  16. Journal of Sound and Vibration v.219 no.1 Natural Frequencies of Noncircular Arches with Rotatory Inertia and Shear Deformation O, S. J.;Lee, B. K.;Lee, I. W.