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On the dynamics of rotating, tapered, visco-elastic beams with a heavy tip mass

  • Zeren, Serkan (Department of Mechanical Engineering, Yeditepe University) ;
  • Gurgoze, Metin (Faculty of Mechanical Engineering, Technical University of Istanbul)
  • 투고 : 2012.01.12
  • 심사 : 2012.12.01
  • 발행 : 2013.01.10

초록

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

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참고문헌

  1. Abolghasemi, M. and Jalali, M.A. (2003), "Attractors of a Rotating Viscoelastic Beam", International Journal of Non-Linear Mechanics, 38, 739-751. https://doi.org/10.1016/S0020-7462(01)00130-5
  2. Arvin, H. and Bakhtiari-Nejad, F. (2011), "Non-linear modal analysis of a rotating beam", International Journal of Non-Linear Mechanics, 46, 877-897. https://doi.org/10.1016/j.ijnonlinmec.2011.03.017
  3. Attarnejad, R. and Shahba, A. (2011a), "Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams; a mechanical solution" Meccanica, 46, 1267-1281. https://doi.org/10.1007/s11012-010-9383-z
  4. Attarnejad, R. and Shahba, A. (2011b), "Basic displacement functions for centrifugally stiffened tapered beam", International Journal of Numerical Methods in Biomedical Engineering, 27, 1385-1397.
  5. Banerjee, J.R., Su, H. and Jackson, D.R. (2006), "Free vibration of a rotating tapered beams using the dynamic stiffness method", Journal of Sound and Vibration, 298, 1034-1054. https://doi.org/10.1016/j.jsv.2006.06.040
  6. Banks, H.T. and Inman, D.J. (1991), "On Damping Mechanisms in Beams", Journal of Applied Mechanics, 58, 716-723. https://doi.org/10.1115/1.2897253
  7. Ganesh, R. and Ganguli, R. (2011), "Physics based basis function for vibration analysis of high speed rotating beams". Structural Engineering and Mechanics, 39, 21-46. https://doi.org/10.12989/sem.2011.39.1.021
  8. Gunda, J.B., Singh, A.P., Chhabra, P.S. and Ganguli, R. (2007), "Free vibration analysis of rotating tapered blades using Fourier-p superelement", Structural Engineering and Mechanics, 27, 243-257. https://doi.org/10.12989/sem.2007.27.2.243
  9. Gurgoze, M., Dogruoglu, A.N. and Zeren, S. (2007), "On the eigencharacteristics of a cantilevered viscoelastic beam carrying a tip mass and its representation by a spring-damper-mass system", Journal of Sound and Vibration, 301, 420-426. https://doi.org/10.1016/j.jsv.2006.10.002
  10. Gurgoze, M. and Zeren, S. (2009), "On the Eigencharacteristics of a Centrifugally Stiffened, Visco-Elastic Beam Carrying a Tip Mass", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 223, 1767-1775. https://doi.org/10.1243/09544062JMES1336
  11. Gurgoze, M. and Zeren, S. (2011), "The Influences of Both Offset and Mass Moment of Inertia of a Tip Mass on the Dynamics of a Centrifugally Stiffened Visco-Elastic Beam", Meccanica, 46, 1401-1412. https://doi.org/10.1007/s11012-010-9396-7
  12. Kumar, A. and Garguli, R. (2009), "Rotating beams and nonrotating beams with shared eigenpair", Journal of Applied Mechanics, 76, 051006:1-051006:14.
  13. Meirovitch, L. (1967), Analytical Methods in Vibrations, The MacMillan Company, New York.
  14. Ozdemir Ozgumus, O. and Kaya, M.O. (2010), "Vibration analysis of a rotating tapered Timoshenko beam using DTM", Meccanica, 45, 33-42. https://doi.org/10.1007/s11012-009-9221-3
  15. Shahba, A., Attarnejad, R. and Zarrinzadeh, H. (2011), "Free vibration analysis of centrifugally stiffened tapered axially functionally graded beams", Mechanics of Advanced Materials and Structures, doi: 10.1080/15376494.2011.627634.
  16. Stevens, K.K. (1966), "On the Parametric Excitation of a Viscoelastic Column", AIAA Journal, 4, 2111-2116. https://doi.org/10.2514/3.3863
  17. Wright, A.D., Smith, C.E., Thresher, R.W. and Wang, J.L.C. (1982), "Vibration modes of centrifugally stiffened beams", Journal of Applied Mechanics, 49, 197-202. https://doi.org/10.1115/1.3161966
  18. Yan, S.X., Zhang, Z.P., Wei, D.J. and Li, X.F. (2011), "Bending vibration of a rotating tapered cantilevers by integral Eq. method", AIAA Journal, 49, 872-876. https://doi.org/10.2514/1.J050572
  19. Younesian, D. and Esmailzadeh, E. (2010), "Non-linear vibration of variable speed rotating viscoelastic beams", Nonlinear Dynamics, 60, 193-205. https://doi.org/10.1007/s11071-009-9589-6
  20. Zarrinzadeh, H., Atternejad, R. and Shahba, A. (2012), "Free vibration of rotating axially functionally graded tapered beams", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 226, 363-379. https://doi.org/10.1177/0954410011413531
  21. Zhu, T.L. (2011), "The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh-Ritz method", Computational Mechanics, 47, 395-408. https://doi.org/10.1007/s00466-010-0550-9

피인용 문헌

  1. Benchmark analytical solutions from beams with shared eigenpair vol.106, 2016, https://doi.org/10.1016/j.ijmecsci.2015.12.017