Structural Engineering and Mechanics

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Dynamic analysis of a beam subjected to an eccentric rolling disk

  • Wu, Jia-Jang (Department of Marine Engineering, College of Maritime, National Kaohsiung Marine University)
  • Received : 2011.11.04
  • Accepted : 2013.08.07
  • Published : 2013.08.25
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Abstract

This paper presents a theory concerning the beam element subjected to an eccentric rolling disk (or simply called the eccentric-disk-loaded beam element) such that the dynamic responses of a beam subjected to an eccentric rolling disk with its inertia force, Coriolis force and centrifugal force considered can be easily determined. To this end, the property matrices of an eccentric-disk-loaded beam element are firstly derived by means of the Lagrange's equations. Then, the overall property matrices of the entire vibrating system are determined by directly adding the property matrices of the eccentric-disk-loaded beam element to the overall ones of the entire beam itself. Finally, the Newmark direct integration method is used to solve the equations of motion for the dynamic responses of a beam subjected to an eccentric rolling disk. Some factors relating to the title problem, such as the eccentricity, radius and rotating speed of the rolling disk, and the Coriolis force and centrifugal force induced by the rolling disk are investigated. Numerical results reveal that the influence of last factors on the dynamic responses of the pinned-pinned beam is significant except the centrifugal force.

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References

  1. Bamford, K. (2010), Moving loads on railway underbridges, including: diagrams of bending moments and shearing forces and tables of equivalent uniform live loads, Nabu Press.
  2. Bathe, K.J. (1982), Finite element procedures in engineering analysis, Prentice-Hall.
  3. Cao, Y.M., Xia, H. and Lombaert, G. (2010), "Solution of moving-load-induced soil vibrations based on the Betti-Rayleigh Dynamic Reciprocal Theorem", Soil Dynamics and Earthquake Engineering, 30, 470-480. https://doi.org/10.1016/j.soildyn.2010.01.003
  4. Charles, M. (2010), Notes on the theory of structure: reactions, moments, shears, moving loads, beams, girders, simple trusses, ISBN: 1990001215382.
  5. Cifuentes, O. (1989), "Dynamic response of a beam excited by a moving mass", Finite Elements in Analysis and Design, 5, 237-246. https://doi.org/10.1016/0168-874X(89)90046-2
  6. Clough, R.W. and Penzien, J. (1993), Dynamics of structures, McGraw-Hill.
  7. Frỳba, L. (1999), Vibration of Solids and Structures under Moving Loads, Thomas Telford Ltd.
  8. Kidarsa, A., Scott, M.H. and Higgins, C.C. (2008), "Analysis of moving loads using force-based finite elements", Finite Elements in Analysis and Design, 44, 214-224. https://doi.org/10.1016/j.finel.2007.11.013
  9. Kim, S.M. (2005), "Stability and dynamic response of Rayleigh beam-columns on an elastic foundation under moving loads of constant amplitude and harmonic variation", Engineering Structures, 27, 869-880. https://doi.org/10.1016/j.engstruct.2005.01.009
  10. Law, S.S. and Zhu, X.Q. (2011), Moving Loads - Dynamic Analysis and Identification Techniques, CRC Press.
  11. Przemieniecki, J.S. (1985), Theory of matrix structural analysis, McGraw-Hill.
  12. Wu, J.J. (2005), "Vibration analyses of a portal frame under the action of a moving distributed mass using moving mass element", International Journal for Numerical Methods in Engineering, 62, 2028-2052. https://doi.org/10.1002/nme.1268
  13. Wu, S.Q. and Law, S.S. (2010), "Moving force identification based on stochastic finite element model", Engineering Structures, 32, 1016-1027. https://doi.org/10.1016/j.engstruct.2009.12.028
  14. Wu, J.S. and Dai, C.W. (1987), "Dynamic responses of multispan nonuniform beam due to moving loads", Journal of Structural Engineering, 113, 458-474. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:3(458)
  15. Wu, J.S., Lee, M.L. and Lai, T.S. (1987), "The dynamic analysis of a flat plate under a moving load by the finite element method", Journal for Numerical Methods in Engineering, 24, 743-762. https://doi.org/10.1002/nme.1620240407
  16. Wu, J.S. and Chiang, L.K. (2003), "Out-of-plane responses of a circular curved Timoshenko beam due to a moving load", International Journal of Solids and Structures, 40, 7425-7448. https://doi.org/10.1016/j.ijsolstr.2003.07.004
  17. Yang, T.Y. (1986), Finite Element Structural Analysis, Prentice-Hall Inc.
  18. Zhai, W. and Song, E. (2010), "Three dimensional FEM of moving coordinates for the analysis of transient vibrations due to moving loads", Computers and Geotechnics, 37, 164-174. https://doi.org/10.1016/j.compgeo.2009.08.007