DOI QR코드

DOI QR Code

Parametric and Combination Resonances of at Straight Pipe with Pulsatile Flow

조화유동을 갖는 직선 파이프의 매개변수공진 해석

  • Published : 2006.12.01

Abstract

The stabilities of a pinned-pinned straight pipe conveying fluid are investigated by complexification-averaging method. The flow is assumed to vary harmonically about a constant mean velocity. Instability conditions of a governing equation are analytically obtained about parametric primary, secondary and combination resonances. The resulted stability conditions show that instabilities exist when the frequency of flow fluctuation is close to one and two times the natural frequency or to the sum of any two natural frequencies. In case that the fluctuated flow frequency is close to the difference of two natural frequencies, instabilities does not exist.

Keywords

Parametric Resonance;Combination Resonance;Flow Induced Vibration;Complexification-averaging Method

References

  1. Housner, G. W., 1952, 'Bending Vibrations of a Pipe Line Containing Flowing Fluid,'Journal of Applied Mechanics, Vol.19, pp.205-209
  2. Benjamin, T. B., 1961, 'Dynamics of a Articulated Pipes Containing Fluid, Part I and II,' Proc. of Royal Society, Ser. A261, pp.475-486
  3. Paidoussis, M. P., 1966, 'Dynamics of Flexible Slender Cylinders in Axial Flow, Part I and II,' Journal of Fluid Mechanics, Vol.26, pp.717-751 https://doi.org/10.1017/S0022112066001496
  4. Cartmell, M., 1990, Introduction to Linear, Parametric and Nonlinear Vibrations, Chapman and Hall, London, UK
  5. Chen, S. S., 1971, 'Dynamic Stability of a Tube Conveying Fluid,' Journal of the Engineering Mechanics Division, Proc. of ASCE, Vol.97, pp.1469-1485
  6. Paidousiss, M. P., Issid, N. T., 'Dynamic Stability of Pipes Conveying Fluid,' Journal of Sound and Vibration, Vol.33(3), 1974, pp.267-294 https://doi.org/10.1016/S0022-460X(74)80002-7
  7. Pak, C. H., Lee, U., Hong, S. C., and Kim T. R., 1991, 'Stability Analysis of Piping System Conveying Unsteady Flow,' Trans. of KSME, VoI.15(5), pp.1512-1521
  8. Lee, U., Pak, C. H., and Hong, S. C., 1991, 'Dynamic Stability and Response Analysis of Piping System with internal Flow,' Trans. of the KSME, Vol.15(6), pp.1861-1991
  9. Lee, U., Pale, C. H., and Hong, S. C., 1995, 'Dynamics of Piping System with Internal Unsteady Flow,' Journal of Sound and Vibration, VoI.180(2), pp.297-311 https://doi.org/10.1006/jsvi.1995.0080
  10. Paidoussis, M. P. and Sundarajan C., 1975, 'Parametric and Combination Resonances of a Pipe ?Conveying Pulsating Fluid,' Trans. of ASME, Journal of Applied Mechanics, Vol.42, pp.780-784 https://doi.org/10.1115/1.3423705
  11. Pak, C. H., Hong, S. C., and Jung, W., 1996, 'Chaotic Vibration of a Straight Pipe Conveying Oscillatory Flow,' Journal of KSNVE, Vol.6, pp.233-244
  12. Pak, C. H., Hong, S. C., and Kim T. J., 1997, 'Chaotic Vibration of a Curved Pipe Conveying Oscillatory Flow,' Journal of KSNVE, Vol.7(3), pp.489-498
  13. Hong, S. C., 2000, 'Chaotic Out-of-Plane Vibrations of Curved Pipe Conveying Oscillatory Flow,' Journal of KSNVE, Vol.10(5), pp.849-858
  14. Hong, S. C. 2004, 'Stability Analysis of a Straight Pipe with Time Dependent Flow,' Trans. of KSME, Vol.28A(3) https://doi.org/10.3795/KSME-A.2004.28.3.318
  15. Nayfeh, A. H. and Mook, D. T., 1979, Nonlinear Oscillations, New York: Wiley
  16. Manevitch, L. I., 2001, 'The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables,' Nonlinear Dynamics, Vol.25, pp.95-109 https://doi.org/10.1023/A:1012994430793
  17. Gendelman, O., Manevitch, L. I., Vakakis, A. F. and M'Closkey R., 2001, 'Energy Pumping in Nonlinear Mechanical Oscillators: Part 1- Dynamics of Underlying Hamiltonian Systems,' Journal of Applied mechanics, Vol.68, pp.34-41 https://doi.org/10.1115/1.1345524
  18. Vakakis, A. F., Manevitch, L. I., Gendelman, O. and Bergman L., 2003, 'Dynamics of Linear Discrete Systems Connected to Local, Essentially Non-linear Attachments,' Journal of sound and vibration, Vol.264, pp.559-577 https://doi.org/10.1016/S0022-460X(02)01207-5
  19. Nayfeh, A. H. and Balachandran, B. 1995, Applied Nonlinear Dynamics, New York: Wiley