Transverse vibration analysis of Euler-Bernoulli beam carrying point masse submerged in fluid media

  • Authors

    • Adil El baroudi ENSAM Angers
    • Fulgence Razafimahery IRMAR Rennes
    2015-05-05
    https://doi.org/10.14419/ijet.v4i2.4570
  • Euler-Bernoulli beam, Fluid-structure interaction, Finite element method, Frequency equation, Inertial coupling.

  • Abstract

    In the present paper, an analytical method is developed to investigate the effects of added mass on natural frequencies and mode shapes of Euler-Bernoulli beams carrying concentrated masse at arbitrary position submerged in a fluid media. A fixed-fixed beams carrying concentrated masse vibrating in a fluid is modeled using the Bernoulli-Euler equation for the beams and the acoustic equation for the fluid. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of a beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results are compared with present method for validation and an acceptable match between them were obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

  • References

    1. [1] K. H. Low, â€Natural frequencies of a beam-mass system in transverse vibration: Rayleigh estimation versus eigenanalysis solutionsâ€, International Journal of Mechanical Sciences, 45, (2003), 981-993.

      [2] M. M. Stanisic, J. C. Hardin, â€On the response of beams to an arbitrary number of concentrated moving massesâ€, Journal of the Franklin Institute, 287, 2, (1969), 115-123.

      [3] P. A. A. Laura, V. H. Cortinez, â€Optimization of eigenvalues in the case of vibrating beams with point massesâ€, Journal of Sound and Vibration, 108, 2, (1986), 346-348.

      [4] M. A. De Rosa and C. Franciosi and M. J. Maurizi, â€On the dynamic behaviour of slender beams with elastic ends carrying a concentrated massâ€, Computers & Structures, 58, 6, (1996), 1145-1159.

      [5] K. H. Low, â€On the eigenfrequencies for mass loaded beams under classical boundary conditionsâ€, Journal of Sound and Vibration, 215, 2, (1998), 381-389.

      [6] Y. Chen, â€On the Vibration of Beams or Rods Carrying a Concentrated Massâ€, J. Appl. Mech, 30, 2, (1963), 310-311.

      [7] W. H. Liu, J. R. Wu, C. C. Huang, â€Free vibration of beams with elastically restrained edges and intermediate concen- trated massesâ€, Journal of Sound and Vibration, 122, 2, (1988), 193-207.

      [8] P. A. A. Laura, P. V. D. Irassar, G. M. Ficcadenti, â€A note on transverse vibrations of continuous beams subject to an axial force and carrying concentrated massesâ€, Journal of Sound and Vibration, 86, 2, (1983), 279-284.

      [9] P. A. A. Laura, J. L. Pombo, E. L. Susemihl, â€A note on the vibration of a clamped-free beam with a mass at the free endâ€, Journal of Sound and Vibration, 37, (1974), 161-168.

      [10] S. Naguleswaran, â€Transverse vibrations of an Euler-Bernoulli uniform beam carrying several particlesâ€, International Journal of Mechanical Science, 44, (2002), 2463-2478.

      [11] C. A. Rossit, P. A. A. Laura, â€Transverse vibrations of a cantilever beam with a spring mass system attached on the free endâ€, Ocean Engineering, 28, (2001), 933-939.

      [12] H. Su, J. R. Banerjee, â€Exact natural frequencies of structures consisting of two part beam-mass systemsâ€, Structural Engineering and Mechanics, 19, 5, (2005), 551-566.

      [13] M. A. De Rosa, N. M. Auciello, M. J. Maurizi, â€The use of Mathematica in the dynamics analysis of a beam with a concentrated mass and dashpotâ€, Journal of Sound and Vibration, 263, (2003), 219-226.

      [14] D. Addessi, W. Lacarbonara, A. Paolone, â€Free in-plane vibrations of highly buckled beams carrying a lumped massâ€, Acta Mechanica, 180, (2005), 133-156.

      [15] K. T. Sundara Raja Iyengar, P. V. Raman, â€Free Vibration of Rectangular Beams of Arbitrary Depthâ€, Acta Mechanica, 32, (1979), 249-259.

      [16] R. Ohayon, C. Soize, Structural Acoustics and Vibration, Academic Press, (1997).

      [17] M. P. Paidoussis, Fluid-Structure Interactions Slender Structures and Axial Flow, volume 1, London Academic Press, (1997).

      [18] J .T. Xing, W. G. Price, M. J. Pomfret, L. H. Yam, â€Natural vibration of a beam-water interaction systemâ€, Journal of Sound and Vibration, 199, 3, (1997), 491-512.

      [19] Comsol Multiphysics 3.5a, User’s Guide and Reference Guide, (2008).

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  • How to Cite

    El baroudi, A., & Razafimahery, F. (2015). Transverse vibration analysis of Euler-Bernoulli beam carrying point masse submerged in fluid media. International Journal of Engineering & Technology, 4(2), 369-380. https://doi.org/10.14419/ijet.v4i2.4570

    Received date: 2015-03-31

    Accepted date: 2015-04-20

    Published date: 2015-05-05