Vibration Analysis of Multi-Span Timoshenko Beams Due to Moving Loads

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  • Published : 1999.11.01


The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.


Multi-Span Beam;Moving Load;Spatial State Equation;Laplace Transform


  1. Journal of Sound and Vibration v.136 Finite Element Analysis of Elastic Beams Subjected to Moving Loads Lin, Y.H.;Trethewey, M.W.
  2. Dynamics of Structures Humar, J.L.
  3. Vibration Problems in Engineering Timoshenko, S.P.;Young, D.H.;Weaver, W.
  4. The Dynamic Behaviour of Structures Warburton, G.B.
  5. Journal of Sound and Vibration v.122 The Dynamic Response of a Rotating Shaft Subject to a Moving Load Katz, R.;Lee, C.W.;Ulsoy, A.G.;Scott, R.A.
  6. Journal of Sound and Vibration v.188 no.4 Response Moments of an Elastic Beam Subjected to Poissonian Moving Loads Zibdeh, H.S.;Rackwitz, R.
  7. Journal of Sound and Vibration Modal Analysis of Multi-Span Timoshenko Beams Connected or Supported by Resilient Joints with Damping Hong, S.-W.;Kim, J.-W.
  8. Journal of Sound and Vibration v.181 no.1 Dynamic Response of a Rotating Timoshenko Shaft Subject to Axial Forces and Moving loads Lee, H.P.
  9. Journal of Sound and Vibration v.96 A Finite Element Method Prediction of the Vibration of a Bridge Subjected to a Moving Vehicle Load Hino, J.;Yoshimura, T.;Konishi, K.
  10. Journal of Sound and Vibration v.212 no.4 An Efficient Algorithm for Dynamic Analysis of Bridges under Moving Vehicles Using a Coupled Modal and Physical Components Approach Henchi, K.;Fafard, M.;Talbot, M.;Dhatt, G.
  11. Journal of Sound and Vibration v.199 no.1 Dynamic Behaviour of Multi-Span Beams Under Moving Loads Henchi, K.;Fafard, M.;Dhatt, G.;Talbot, M.
  12. 대한기계학회논문집 A권 v.23 no.2 다단 회전체 베어링계를 위한 엄밀한 동적 해석 방법 박종혁;홍성욱
  13. Analytical Methods in Vibration Meirovitch, L.
  14. Lambda-matrices and Vibrating Systems Lancaster, P.
  15. Journal of Sound and Vibration v.212 no.3 Vibration of Multi-span Non-Uniform Beams Under Moving Loads by Using Modified Beam Vibration Functions Zheng, D.Y.;Cheung, Y.K.;Au, F.T.K.;Cheng, Y.S.
  16. Journal of Sound and Vibration v.213 no.1 Random Vibration of Multi-Span Timoshenko Beam Due to a Moving Load Wang, R.-T.;Lin, T.-Y.