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Acta Mechanica Sinica

, Volume 34, Issue 5, pp 963–969 | Cite as

Gyroscopic modes decoupling method in parametric instability analysis of gyroscopic systems

  • Y. J. Qian
  • X. D. Yang
  • H. Wu
  • W. Zhang
  • T. Z. Yang
Research Paper
  • 121 Downloads

Abstract

Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms. In this study, a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings. Taking the axially moving string as an example, the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes, and the results are compared to show the advantages and disadvantages of each method.

Keywords

Axially moving material Decoupling of gyroscopic modes Parametric instability Perturbation method Gyroscopic system 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11772009, 11672007) and the Beijing Municipal Natural Science Foundation (Grant 3172003).

References

  1. 1.
    Mirtalaie, S.H., Hajabasi, M.A.: A new methodology for modeling and free vibrations analysis of rotating shaft based on the timoshenko beam theory. J. Vib. Acoust. 138, 021012 (2016)CrossRefGoogle Scholar
  2. 2.
    Shahgholi, M., Khadem, S.E., Bab, S.: Nonlinear vibration analysis of a spinning shaft with multi-disks. Meccanica 50, 2293–2307 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Guven, U., Celik, A.: On transverse vibrations of functionally graded isotropic linearly elastic rotating solid disks. Mech. Res. Commun. 28, 271–276 (2001)CrossRefGoogle Scholar
  4. 4.
    Khorasany, R.M.H., Hutton, S.G.: On the equilibrium configurations of an elastically constrained rotating disk: an analytical approach. Mech. Res. Commun. 38, 288–293 (2011)CrossRefGoogle Scholar
  5. 5.
    Invernizzi, D., Dozio, L.: A fully consistent linearized model for vibration analysis of rotating beams in the framework of geometrically exact theory. J. Sound Vib. 370, 351–371 (2016)CrossRefGoogle Scholar
  6. 6.
    Ghafarian, M., Ariaei, A.: Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method. Int. J. Mech. Sci. 107, 93–109 (2016)CrossRefGoogle Scholar
  7. 7.
    Bediz, B., Romero, L.A., Ozdoganlar, O.B.: Three dimensional dynamics of rotating structures under mixed boundary conditions. J. Sound Vib. 358, 176–191 (2015)CrossRefGoogle Scholar
  8. 8.
    Wickert, J.A., Mote, C.D.: Classical vibration analysis of axially moving continua. J. Appl. Mech. T Asme 57, 738–744 (1990)CrossRefGoogle Scholar
  9. 9.
    Chen, L.-Q.: Analysis and control of transverse vibrations of axially moving strings. Appl. Mech. Rev. 58, 91–116 (2005)CrossRefGoogle Scholar
  10. 10.
    Chen, L.-Q., Yang, X.-D.: Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. Int. J. Solids Struct. 42, 37–50 (2005)CrossRefGoogle Scholar
  11. 11.
    Ding, H., Chen, L.-Q., Yang, S.-P.: Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load. J. Sound Vib. 331, 2426–2442 (2012)CrossRefGoogle Scholar
  12. 12.
    Ding, H., Zhang, G.-C., Chen, L.-Q.: Supercritical equilibrium solutions of axially moving beams with hybrid boundary conditions. Mech. Res. Commun. 38, 52–56 (2011)CrossRefGoogle Scholar
  13. 13.
    Wu, H., Chen, X.W., Fang, Q., et al.: Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part II: structural stability analyses. Acta. Mech. Sin. 30, 943–955 (2014)CrossRefGoogle Scholar
  14. 14.
    Kurki, M., Jeronen, J., Saksa, T., et al.: The origin of in-plane stresses in axially moving orthotropic continua. Int. J. Solids Struct. 81, 43–62 (2016)CrossRefGoogle Scholar
  15. 15.
    Hatami, S., Ronagh, H.R., Azhari, M.: Exact free vibration analysis of axially moving viscoelastic plates. Comput. Struct. 86, 1738–1746 (2008)CrossRefGoogle Scholar
  16. 16.
    Yang, X.-D., Wu, H., Qian, Y.-J., et al.: Nonlinear vibration analysis of axially moving strings based on gyroscopic modes decoupling. J. Sound Vib. 393, 308–320 (2017)CrossRefGoogle Scholar
  17. 17.
    Ghayesh, M.H., Farokhi, H.: Nonlinear dynamical behavior of axially accelerating beams: three-dimensional analysis. J. Comput. Nonlinear Dyn. 11, 011010 (2016)CrossRefGoogle Scholar
  18. 18.
    Banerjee, J.R., Kennedy, D.: Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects. J. Sound Vib. 333, 7299–7312 (2014)CrossRefGoogle Scholar
  19. 19.
    Shahgholi, M., Khadem, S.E., Bab, S.: Free vibration analysis of a nonlinear slender rotating shaft with simply support conditions. Mech. Mach. Theory 82, 128–140 (2014)CrossRefGoogle Scholar
  20. 20.
    Yang, X.-D., Yang, S., Qian, Y.-J., et al.: Modal analysis of the gyroscopic continua: comparison of continuous and discretized models. J. Appl. Mech. T Asme 83, 084502 (2016)CrossRefGoogle Scholar
  21. 21.
    Yang, X.-D., Liu, M., Qian, Y.-J., et al.: Linear and nonlinear modal analysis of the axially moving continua based on the invariant manifold method. Acta Mech. 228, 465–474 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Huang, J.L., Su, R.K.L., Li, W.H., et al.: Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances. J. Sound Vib. 330, 471–485 (2011)CrossRefGoogle Scholar
  23. 23.
    Kesimli, A., Ozkaya, E., Bagdatli, S.M.: Nonlinear vibrations of spring-supported axially moving string. Nonlinear Dyn. 81, 1523–1534 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Malookani, R.A., van Horssen, W.T.: On resonances and the applicability of Galerkin’s truncation method for an axially moving string with time-varying velocity. J. Sound Vib. 344, 1–17 (2015)CrossRefGoogle Scholar
  25. 25.
    Chen, L.-Q., Tang, Y.-Q., Zu, J.W.: Nonlinear transverse vibration of axially accelerating strings with exact internal resonances and longitudinally varying tensions. Nonlinear Dyn. 76, 1443–1468 (2014)CrossRefGoogle Scholar
  26. 26.
    Sahoo, B., Panda, L.N., Pohit, G.: Combination, principal parametric and internal resonances of an accelerating beam under two frequency parametric excitation. Int. J. Nonlinear Mech. 78, 35–44 (2016)CrossRefGoogle Scholar
  27. 27.
    Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim (2004)zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Y. J. Qian
    • 1
  • X. D. Yang
    • 1
  • H. Wu
    • 1
  • W. Zhang
    • 1
  • T. Z. Yang
    • 2
  1. 1.College of Mechanical EngineeringBeijing University of TechnologyBeijingChina
  2. 2.Department of MechanicsTianjing UniversityTianjingChina

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