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Nonlinear dynamic response and transmissibility of a flexible rotor system mounted on viscoelastic elements

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Abstract

In this paper, the three-dimensional nonlinear dynamics and force transmissibility characteristics of a flexible shaft-disk rotor system are investigated numerically. The rotor system is comprised of a flexible shaft supporting a rigid disk, and the shaft ends are mounted on viscoelastic elements (bearing/support). The dynamic model of the system is developed considering the coupled axial and bending–bending elastic motions of the shaft while the disk is modeled as a rigid body. The equations of motion (EOM) obtained using Lagrange’s equation are discretized using the assumed mode method utilizing large number of modes to examine the system dynamics accurately for multiple resonance regions. The EOM are then linearized to obtain the natural frequencies to construct the Campbell diagrams and investigate the influence of the bearing stiffness and disk location on critical speeds and whirling modes. The harmonic balance method combined with the pseudo-arclength continuation method is used to construct the nonlinear frequency response and force transmissibility curves due to disk unbalance force. The effects of the bearing stiffness and damping, unbalance force magnitude and disk location on the nonlinear multi-mode primary frequency response and force transmissibility are then thoroughly investigated.

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References

  1. Sun, C., Chen, Y., Hou, L.: Steady-state response characteristics of a dual-rotor system induced by rub-impact. Nonlinear Dyn. 86(1), 91–105 (2016)

    Article  Google Scholar 

  2. Chun, S.-B., Lee, C.-W.: Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed modes method. J. Sound Vib. 189(5), 587–608 (1996)

    Article  Google Scholar 

  3. Phadatare, H., Choudhary, B., Pratiher, B.: Evaluation of nonlinear responses and bifurcation of a rotor-bearing system mounted on moving platform. Nonlinear Dyn. 90(1), 493–511 (2017)

    Article  Google Scholar 

  4. Younesian, D., Jafari, A., Serajian, R.: Effects of the bogie and body inertia on the nonlinear wheel-set hunting recognized by the hopf bifurcation theory. Int. J. Automot. Eng. 1(3), 186–196 (2011)

    Google Scholar 

  5. Serajian, R.: Parameters changing influence with different lateral stiffnesses on nonlinear analysis of hunting behavior of a bogie. J. Meas. Eng. 1(4), 195–206 (2013)

    Google Scholar 

  6. Friswell, M.I., Penny, J.E., Garvey, S.D., Lees, A.W.: Dynamics of Rotating Machines. Cambridge University Press, New York (2010)

    Book  MATH  Google Scholar 

  7. Nelson, F.: Rotor dynamics without equations. Int. J. COMADEM 10(3), 2 (2007)

    Google Scholar 

  8. Yu, T.-J., Zhou, S., Yang, X.-D., Zhang, W.: Global dynamics of a flexible asymmetrical rotor. Nonlinear Dyn. 91(2), 1041–1060 (2018)

    Article  MATH  Google Scholar 

  9. Pai, P.F., Qian, X., Du, X.: Modeling and dynamic characteristics of spinning rayleigh beams. Int. J. Mech. Sci. 68, 291–303 (2013)

    Article  Google Scholar 

  10. Roques, S., Legrand, M., Cartraud, P., Stoisser, C., Pierre, C.: Modeling of a rotor speed transient response with radial rubbing. J. Sound Vib. 329(5), 527–546 (2010)

    Article  Google Scholar 

  11. Sheu, G., Yang, S.-M.: Dynamic analysis of a spinning rayleigh beam. Int. J. Mech. Sci. 47(2), 157–169 (2005)

    Article  MATH  Google Scholar 

  12. Zu, J.W.-Z., Han, R.P.: Natural frequencies and normal modes of a spinning timoshenko beam with general boundary conditions. J. Appl. Mech. 59(2S), S197–S204 (1992)

    Article  Google Scholar 

  13. Khadem, S., Shahgholi, M., Hosseini, S.: Primary resonances of a nonlinear in-extensional rotating shaft. Mech. Mach. Theory 45(8), 1067–1081 (2010)

    Article  MATH  Google Scholar 

  14. Shahgholi, M., Khadem, S.: Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity. Mech. Mach. Theory 51, 131–144 (2012)

    Article  Google Scholar 

  15. Khanlo, H., Ghayour, M., Ziaei-Rad, S.: Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator. Commun. Nonlinear Sci. Numer. Simul. 16(1), 566–582 (2011)

    Article  Google Scholar 

  16. Khanlo, H., Ghayour, M., Ziaei-Rad, S.: The effects of lateral-torsional coupling on the nonlinear dynamic behavior of a rotating continuous flexible shaft-disk system with rub-impact. Commun. Nonlinear Sci. Numer. Simul. 18(6), 1524–1538 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shad, M.R., Michon, G., Berlioz, A.: Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending. Appl. Math. Modell. 35(5), 2145–2159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zou, D., Rao, Z., Ta, N.: Coupled longitudinal-transverse dynamics of a marine propulsion shafting under superharmonic resonances. J. Sound Vib. 346, 248–264 (2015)

    Article  Google Scholar 

  19. Phadatare, H., Maheshwari, V., Vaidya, K., Pratiher, B.: Large deflection model for nonlinear flexural vibration analysis of a highly flexible rotor-bearing system. Int. J. Mech. Sci. 134, 532–544 (2017)

    Article  Google Scholar 

  20. Tiaki, M.M., Hosseini, S., Zamanian, M.: Nonlinear forced vibrations analysis of overhung rotors with unbalanced disk. Arch. Appl. Mech. 86(5), 797–817 (2016)

    Article  Google Scholar 

  21. Shabaneh, N., Zu, J.: Nonlinear dynamic analysis of a rotor shaft system with viscoelastically supported bearings. J. Vib. Acoust. Trans. ASME 125(3), 290–298 (2003)

    Article  Google Scholar 

  22. Ji, Z., Zu, J.: Method of multiple scales for vibration analysis of rotor-shaft systems with non-linear bearing pedestal model. J. Sound Vib. 218(2), 293–305 (1998)

    Article  Google Scholar 

  23. Ribeiro, E.A., Pereira, J.T., Bavastri, C.A.: Passive vibration control in rotor dynamics: optimization of composed support using viscoelastic materials. J. Sound Vib. 351, 43–56 (2015)

    Article  Google Scholar 

  24. Lu, Z., Brennan, M.J., Chen, L.-Q.: On the transmissibilities of nonlinear vibration isolation system. J. Sound Vib. 375, 28–37 (2016)

    Article  Google Scholar 

  25. De Silva, C.W.: Vibration: Fundamentals and Practice. CRC Press, Boca Raton (2006)

    Book  Google Scholar 

  26. Kirk, R.G., Gunter, E.J.: The effect of support flexibility and damping on the synchronous response of a single-mass flexible rotor. J. Eng. Ind. 94(1), 221–232 (1972)

    Article  Google Scholar 

  27. Panda, K., Dutt, J.: Optimum support characteristics for rotor-shaft system with preloaded rolling element bearings. J. Sound Vib. 260(4), 731–755 (2003)

    Article  Google Scholar 

  28. Ribeiro, E.A., de Oliveira Lopes, E.M., Bavastri, C.A.: A numerical and experimental study on optimal design of multi-dof viscoelastic supports for passive vibration control in rotating machinery. J. Sound Vib. 411, 346–361 (2017)

    Article  Google Scholar 

  29. Arias-Montiel, M., Silva-Navarro, G., Antonio-García, A.: Active vibration control in a rotor system by an active suspension with linear actuators. J. Appl. Res. Technol. 12(5), 898–907 (2014)

    Article  Google Scholar 

  30. Shi, P., McPhee, J., Heppler, G.: A deformation field for Euler-Bernoulli beams with applications to flexible multibody dynamics. Multibody Syst. Dyn. 5(1), 79–104 (2001)

    Article  MATH  Google Scholar 

  31. Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics. Wiley, Hoboken (2008)

    MATH  Google Scholar 

  32. Ghayesh, M.H.: Stability and bifurcations of an axially moving beam with an intermediate spring support. Nonlinear Dyn. 69(1–2), 193–210 (2012)

    Article  MathSciNet  Google Scholar 

  33. Al-Solihat, M.K., Nahon, M., Behdinan, K.: “Three-dimensional nonlinear coupled dynamic modeling of a tip-loaded rotating cantilever. J. Vib. Control 1077546317753058 (2018)

  34. Meirovitch, L., Tuzcu, I.: Integrated approach to the dynamics and control of maneuvering flexible aircraft. In: NASA Langley Research Center, Hampton, VA, Tech. Rep. NASA/CR-2003-211748 (2003)

  35. Meirovitch, L., Stemple, T.: Hybrid equations of motion for flexible multibody systems using quasicoordinates. J. Guid. Control Dyn. 18(4), 678–688 (1995)

    Article  MATH  Google Scholar 

  36. Rao, S.S.: Vibration of Continuous Systems. Wiley, New York (2007)

    Google Scholar 

  37. Karnovsky, I.A., Lebed, O.I., Lebed, O.: Formulas for Structural Dynamics: Tables, Graphs and Solutions. McGraw-Hill, New York (2000)

    Google Scholar 

  38. Thomsen, J.J.: Vibrations and Stability: Advanced Theory, Analysis, and Tools. Springer, Heidelberg (2013)

    Google Scholar 

  39. Dimitriadis, G.: Introduction to Nonlinear Aeroelasticity. Wiley, Hoboken (2017)

    Book  Google Scholar 

  40. Duchemin, M., Berlioz, A., Ferraris, G.: Dynamic behavior and stability of a rotor under base excitation. J. Vib. Acoust. 128(5), 576–585 (2006)

    Article  Google Scholar 

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Acknowledgements

The financial support granted by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant RGPIN 217525) is gratefully appreciated.

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  1. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada

    Mohammed Khair Al-Solihat & Kamran Behdinan

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  1. Mohammed Khair Al-Solihat
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Correspondence to Mohammed Khair Al-Solihat.

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Al-Solihat, M.K., Behdinan, K. Nonlinear dynamic response and transmissibility of a flexible rotor system mounted on viscoelastic elements. Nonlinear Dyn 97, 1581–1600 (2019). https://doi.org/10.1007/s11071-019-05078-3

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  • DOI: https://doi.org/10.1007/s11071-019-05078-3

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