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Transverse runout in flexible disk rotating at periodically varying angular speed

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Abstract

Under consideration of initial unstressed transverse runout, governing equation of a flexible disk rotating at periodically varying angular speed is modeled as a parametrically excited system, and steady state deflection and resonance of the disk is investigated by the harmonic balance method. The investigation shows that the initial transverse runout of a given disk mode affects the steady state deflection of the mode itself more prominently than other modes, and the deflection component fluctuating in high-frequency is weak and can be neglected in analysis. The disk resonates when the integer multiple frequency of angular speed variation around the disk natural frequency in the frame fixed on the disk. And each integer multiple frequency results in twin resonance peaks with increasing variation amplitude and constant part of the angular speed. The angular speed variation amplitude enlarges the resonance peaks.

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References

  1. Jia HS (2000) Analysis of transverse runout in rotating flexible disks by using Galerkin’s method. Int J Mech Sci 42:237–248

    Article  MATH  Google Scholar 

  2. Chen JS, Lin CC (2005) Axisymmetrical snapping of a spinning nonflat disk. Trans ASME J Appl Mech 72:879–886

    Article  MATH  Google Scholar 

  3. Chen JS, Chang YY (2007) On the unsymmetrical deformation and reverse snapping of a spinning non-flat disk. Int J Non-linear Mech 42:1000–1009

    Article  Google Scholar 

  4. Fung RF (1997) Vibration and variable structure control with integral compensation in a non-constant rotating disk system. J Sound Vib 199:223–236

    Article  ADS  Google Scholar 

  5. Hansen MH (2000) Effect of high-frequency excitation on natural frequencies of spinning discs. J Sound Vib 234:577–589

    Article  ADS  Google Scholar 

  6. Hsu CS (1963) On the parametric excitation of a dynamic system having multiple degrees of freedom. Trans ASME J Appl Mech 30:367–372

    Article  MATH  Google Scholar 

  7. Zajaczkowski J, Lipinski J (1979) Vibrations of parametrically excited systems. J Sound Vib 63:1–7

    Article  ADS  MATH  Google Scholar 

  8. Takahashi K (1981) An approach to investigate the instability of the multiple-degree-of-freedom parametric dynamic systems. J Sound Vib 78:519–529

    Article  ADS  MATH  Google Scholar 

  9. Leung AYT (1989) Stability boundaries for parametrically excited systems by dynamic stiffness. J Sound Vib 132:265–273

    Article  ADS  Google Scholar 

  10. Seyranian AP, Mailybaev AA (2003) Multiparameter stability theory with mechanical applications. World Scientific, Singapore

    Book  MATH  Google Scholar 

  11. Mehidi N (2007) Averaging and periodic solutions in the plane and parametrically excited pendulum. Meccanica 42:403–407

    Article  MathSciNet  MATH  Google Scholar 

  12. Hegazy UH (2009) Dynamics and control of a self-sustained electromechanical seismographs with time-varying stiffness. Meccanica 44:355–368

    Article  MATH  Google Scholar 

  13. Kamel M, Bauomy HS (2010) Nonlinear behavior of a rotor-AMB system under multi-parametric excitations. Meccanica 45:7–22

    Article  MATH  Google Scholar 

  14. Young TH (1992) Nonlinear transverse vibrations and stability of spinning disks with nonconstant spinning rate. Trans ASME J Vib Acoust 114:506–513

    Article  Google Scholar 

  15. Pei YC, Tan QC (2009) Parametric instability of flexible disk rotating at periodically varying angular speed. Meccanica 44:711–720

    Article  MathSciNet  Google Scholar 

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Correspondence to Yong-Chen Pei.

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Pei, YC., He, FJ. & He, L. Transverse runout in flexible disk rotating at periodically varying angular speed. Meccanica 46, 303–311 (2011). https://doi.org/10.1007/s11012-010-9309-9

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  • DOI: https://doi.org/10.1007/s11012-010-9309-9

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