Advertisement

Journal of Mechanical Science and Technology

, Volume 19, Issue 9, pp 1731–1741 | Cite as

Influence of tip mass on dynamic behavior of cracked cantilever pipe conveying fluid with moving mass

  • Han-Ik Yoon
  • In-Soo Son
Article

Abstract

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange’s equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

Key Words

Dynamic Behavior Open Crack Cantilever Pipe Conveying Fluid Moving Mass Tip Mass Euler-Bernoulli Beam Flexibility Matrix 

Nomenclature

ac

Maximum depth of crack

A

Cross-sectional area

b

Half-length of crack

C

Flexibility matrix

d

Tip-displacement of pipe, dimensionless

Ff

Tangential follower force

Jo*

Moment of inertia of tip mass, dimensionless

KI

Stress intensity factor (fracture mode I)

KR

Rotating spring coefficient

k

Number of segment

m

Mass per unit length of pipe

mf

Fluid mass per unit length of pipe

mm

Moving mass

mp

Tip mass

q

Deflection of pipe

u

Velocity of fluid

U

Velocity of fluid, dimensionless

v

Velocity of moving mass

V

Velocity of moving mass, dimensionless

μm

Ratio of tip mass to its moment of inertia

θ*

Half-angle of crack, dimensionless

f

Distance measured along pipe, dimensionless

ξc

Crack position, dimensionless

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benjamin, T. B., 1961, “Dynamics of a System of Articulated Pipes Conveying Fluid (I. Theory),”Proceedings of the Royal Society (London), Series A, Vol. 261, pp. 457–468.CrossRefMathSciNetGoogle Scholar
  2. Carlson, R. L., 1974, “An Experimental Study of the Parametric Excitation of a Tensioned Sheet with a Crack-like Opening,”Experimental Mechanics, Vol. 14, pp. 452–458.CrossRefGoogle Scholar
  3. Chondros, T. G. and Dimarogonas, A. D., 1989, “Dynamic Sensitivity of Structures to Cracks,”J. Vibration and Acoustics, Stress and Reliability in Design 111, pp. 251-256.Google Scholar
  4. Chondros, T. G. and Dimarogonas, A. D., 1998, “Vibration of a Cracked Cantilever Beam,”J. Vibration and Acoustics, Transactions of the American Society of Mechanical Engineers 120, pp. 742-746.Google Scholar
  5. Christides, S. and Barr, A. D. S., 1984, “One- dimensional Theory of Cracked Bernoulli-Euler Beams,”Int. J. Mechanical Sciences, Vol. 26, pp. 639–648.CrossRefGoogle Scholar
  6. Dado, M. H. F. and Abuzeid, O., 2003, “Coupled Transverse and Axial Vibratory Behaviour of Cracked Beam with End Mass and Rotary Inertia,”J. Sound and Vibration, Vol. 261, pp. 675–696.CrossRefGoogle Scholar
  7. Gudmundson, P., 1983, “The Dynamic Behaviour of Slender Structures with Cross-sectional Cracks,”Journal of Mechanics Physics Solids, Vol. 31, pp. 329–345.MATHCrossRefGoogle Scholar
  8. Kisa, M. and Brandon, J., 2000, “The Effects of Closure of Cracks on the Dynamics of a Cracked Cantilever Beam,”J. Sound and Vibration, Vol. 238, No. 1, pp. 1–18.CrossRefGoogle Scholar
  9. Langthjem, M. A. and Sugiyama, Y., 1999, “Vibration and Stabiltiy Analysis of cantilevered Two-pipe Systems Conveying Different Fluids,”J. Fluids and Structures, Vol. 13, pp. 251–268.CrossRefGoogle Scholar
  10. Lee, H. P., 1996, “The Dynamic Response of a Timoshenko Beam Subjected to a Moving Mass,”J. Sound and Vibration, Vol. 198, No. 2, pp. 249–256.CrossRefGoogle Scholar
  11. Lim, J. H., Jung, G. C. and Choi, Y. S., 2003, “Nonlinear Dynamic Analysis of a Cantilever Tube Conveying Fluid with System Identification,”KSME Int. J., Vol. 17, No. 12, pp. 1994–2003.Google Scholar
  12. Liu, D., Gurgenci, H. and Veidt, M., 2003, “Crack Detection in Hollow Section Structures Through Coupled Response Measurements,”J. Sound and Vibration, Vol. 261. pp. 17–29.CrossRefGoogle Scholar
  13. Mahmoud, M. A. and Abou Zaid, M. A., 2002, “Dynamic Response of a Beam with a Crack Subject to a Moving Mass,”J. Sound and Vibration, Vol. 256, No. 4, pp. 591–603.CrossRefGoogle Scholar
  14. Ostachowicz, W. M. and Krawczuk, M., 1991, “Analysis of the Effect of Cracks on the Natural Frequencies of a Cantilever Beam,”J. Sound and Vibration, Vol. 150, pp. 191–201.CrossRefGoogle Scholar
  15. Rao, S., 1995, “Mechanical Vibrations,”Addison-Wesley (3rd Ed.).Google Scholar
  16. Shen, M. H. H. and Pierre, C., 1990, “Natural Modes of Bernoulli-Euler Beams with Symmetric Cracks,”J. Sound and Vibration, Vol. 138, pp. 115–134.CrossRefGoogle Scholar
  17. Stanisic, M. M., 1985, “On a New Theory of the Dynamic Behavior of the Structures Carrying Moving Masses,”Ingenieur-Archiv, Vol. 55, pp. 176–185.MATHCrossRefGoogle Scholar
  18. Yoon, H. I., Jin, J. T. and Son, I. S., 2004, “A Study on Dynamic Behavior of Simply Supported Fluid Flow Pipe with Crack and Moving Mass,”J. KSME in Korea, Vol. 28, No. 4, pp. 419–426.Google Scholar
  19. Yoon, H. I. and Son, I. S., 2004, “Dynamic Behavior of Cracked Pipe Conveying Fluid with Moving Mass Based on Timoshenko Beam Theory,”KSME Int. J., Vol. 18, No. 12, pp. 2216–2224.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2005

Authors and Affiliations

  1. 1.Division of Mechanical EngineeringDong-eui UniversityBusanjin-GuKorea
  2. 2.The Center for Industrial TechnologyDong-eui UniversityBusanjin-GuKorea

Personalised recommendations