Structural Engineering and Mechanics

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An exact solution for free vibrations of a non-uniform beam carrying multiple elastic-supported rigid bars

  • Lin, Hsien-Yuan (Department of Mechanical Engineering, Cheng Shiu University)
  • Received : 2009.04.20
  • Accepted : 2009.11.05
  • Published : 2010.03.10
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Abstract

The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-step beam carrying multiple rigid bars, with each of the rigid bars possessing its own mass and rotary inertia, fixed to the beam at one point and supported by a translational spring and/or a rotational spring at another point. Where the fixed point of each rigid bar with the beam does not coincide with the center of gravity the rigid bar or the supporting point of the springs. The effects of the distance between the "fixed point" of each rigid bar and its center of gravity (i.e., eccentricity), and the distance between the "fixed point" and each linear spring (i.e., offset) are studied. For a beam carrying multiple various concentrated elements, the magnitude of each lumped mass and stiffness of each linear spring are the well-known key parameters affecting the free vibration characteristics of the (loaded) beam in the existing literature, however, the numerical results of this paper reveal that the eccentricity of each rigid bar and the offset of each linear spring are also the predominant parameters.

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References

  1. Farghaly, S.H. (1992), "Bending vibrations of an axially loaded cantilever beam with an elastically mounted end mass of finite length", J. Sound Vib., 156, 373-380. https://doi.org/10.1016/0022-460X(92)90706-4
  2. Gurgoze, M. (1986a), "On the approximate determination of the fundamental frequency of restrained cantilever beam carrying a tip heavy body", J. Sound Vib., 105, 443-449. https://doi.org/10.1016/0022-460X(86)90170-7
  3. Gurgoze, M. and Batan, H. (1986b), "A note on the vibrations of a restrained cantilever beam carrying a tip heavy body", J. Sound Vib., 106, 533-536. https://doi.org/10.1016/0022-460X(86)90197-5
  4. Lin, H.Y. (2008), "On the natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of concentrated elements", Struct. Eng. Mech., 29(5), 531-550. https://doi.org/10.12989/sem.2008.29.5.531
  5. Liu, W.H. and Huang, C.C. (1988), "Vibrations of constrained beam carrying a heavy tip body", J. Sound Vib., 123, 15-29. https://doi.org/10.1016/S0022-460X(88)80074-9
  6. Maurizi, M.J., Belles, P. and Rosales, M. (1990), "A note on free vibrations of a constrained cantilever beam with a tip mass of finite length", J. Sound Vib., 138, 170-172. https://doi.org/10.1016/0022-460X(90)90711-8
  7. Naguleswaran, S. (2002), "Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three step changes in cross-section", Int. J. Mech. Sci., 44, 2541-2555. https://doi.org/10.1016/S0020-7403(02)00190-X
  8. Rama Bhat, B. and Wagner, H. (1976), "Natural frequencies of a uniform cantilever with a tip mass slender in the axial direction", J. Sound Vib., 45, 304-307. https://doi.org/10.1016/0022-460X(76)90606-4
  9. Wu, J.S. and Chen, C.T. (2007a), "A lumped-mass TMM for free vibration analysis of a multiple-step beam carrying eccentric tip masses with rotary inertias", J. Sound Vib., 301, 878-897. https://doi.org/10.1016/j.jsv.2006.10.022
  10. Wu, J.S. and Chen, C.T. (2007b), "A continuous-mass TMM for free vibration analysis of a non- uniform beam with various boundary conditions and carrying multiple concentrated elements", J. Sound Vib., 311, 1420-1430.
  11. Zhou, D. (1997), "The vibrations of a cantilever beam carrying a heavy tip mass with elastic supports", J. Sound Vib., 206, 275-279. https://doi.org/10.1006/jsvi.1997.1087

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