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Analysis of a cantilever bouncing against a stop according to Timoshenko beam theory

  • Tsai, Hsiang-Chuan (Department of Construction Engineering, National Taiwan Institute of Technology) ;
  • Wu, Ming-Kuen (Department of Construction Engineering, National Taiwan Institute of Technology)
  • Published : 1997.05.25

Abstract

The bouncing of a cantilever with the free end pressed against a stop can create high-frequency vibration that the Bernoulli-Euler beam theory is inadequate to solve. An analytic procedure is presented using Timoshenko beam theory to obtain the non-linear response of a cantilever supported by an elastic stop with clearance at the free end. Through a numerical example, the bouncing behavior of the Timoshenko and Bernoulli-Euler beam models are compared and discussed.

Keywords

Acknowledgement

Supported by : National Science Council

References

  1. Aprahamian, R. and Evensen, D.A. (1970), "Applications of holography to dynamics: high-frequency vibrations of beams", Journal of Applied Mechanics ASME, 37, 287-291. https://doi.org/10.1115/1.3408503
  2. Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, 2nd edotopm, McGraw-Hill, Singapore.
  3. Cowper, G.R. (1966), "The shear coefficient in Timoshenko's beam theory", Journal of Applied Mechanics ASME, 33, 335-340. https://doi.org/10.1115/1.3625046
  4. Herrmann, G. (1955), "Forced motions of Timoshenko beams", Journal of Applied Mechanics ASME, 22, 53-56.
  5. Huang, T.C. (1961), "The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions", Journal of Applied Mechanics ASME, 28, 579-584. https://doi.org/10.1115/1.3641787
  6. Kelly, J.M. (1967), "The impact of a mass on a beam", International Journal of Solids and Structures, 3, 191-196. https://doi.org/10.1016/0020-7683(67)90068-6
  7. Lo, C.C. (1980), "A cantilever beam chattering against a stop", Journal of Sound and Vibration, 69, 245-255. https://doi.org/10.1016/0022-460X(80)90609-4
  8. Maison, B.F. and Kasai, K. (1990), "Analysis for type of structural pounding", Journal of Structural Engineering ASCE, 116, 957-977. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:4(957)
  9. Masri, S.F., Mariamy, Y.A. and Anderson, J.C. (1981), "Dynamics response of a beam with a geometric nonlinearity", Journal of Applied Mechanics ASME, 48, 404-410. https://doi.org/10.1115/1.3157630
  10. Salmon, M.A., Verma, V.K. and Youtsos, T.G. (1985), "Elastic analysis of beam-support impact", Journal of Pressure Vessel Technology ASME, 107, 64-67. https://doi.org/10.1115/1.3264407
  11. Shaw, S.W. (1985), "Forced vibrations of a beam with one-side amplitude constraint:theory and experiment", Journal of Sound and Vibration, 99, 199-212. https://doi.org/10.1016/0022-460X(85)90357-8
  12. Tsai, H.-C., Lin, C.-W. and Tang, Y.K. (1989), "Response spectrum analysis of multiple support excitation on piping system with gapped supports", ASME Presure Vessel and Piping Conference, Honolulu, PVP-182, 317-324.