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



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 



Maximum depth of crack


Cross-sectional area


Half-length of crack


Flexibility matrix


Tip-displacement of pipe, dimensionless


Tangential follower force


Moment of inertia of tip mass, dimensionless


Stress intensity factor (fracture mode I)


Rotating spring coefficient


Number of segment


Mass per unit length of pipe


Fluid mass per unit length of pipe


Moving mass


Tip mass


Deflection of pipe


Velocity of fluid


Velocity of fluid, dimensionless


Velocity of moving mass


Velocity of moving mass, dimensionless


Ratio of tip mass to its moment of inertia


Half-angle of crack, dimensionless


Distance measured along pipe, dimensionless


Crack position, dimensionless


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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

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