Structural Engineering and Mechanics

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Detection of crack in L-shaped pipes filled with fluid based on transverse natural frequencies

  • Murigendrappa, S.M. (Mechanical Engineering Department, Indian Institute of Technology Bombay) ;
  • Maiti, S.K. (Mechanical Engineering Department, Indian Institute of Technology Bombay) ;
  • Srirangarajan, H.R. (Mechanical Engineering Department, Indian Institute of Technology Bombay)
  • Received : 2003.12.18
  • Accepted : 2005.09.28
  • Published : 2005.12.20
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Abstract

The possibility of detecting a crack in L-shaped pipes filled with fluid based on measurement of transverse natural frequencies is examined. The problem is solved by representing the crack by a massless rotational spring, simulating the out-of-plane transverse vibration only without solving the coupled torsional vibration and using the transfer matrix method for solution of the governing equation. The theoretical solutions are verified by experiments. The cracks considered are external, circumferentially oriented and have straight front. Pipes made of aluminium and mild steel are tested with water as internal fluid. Crack size to pipe thickness ratio ranging from 0.20 to 0.57 and fluid (gauge) pressure in the range of 0 to 10 atmospheres are examined. The rotational spring stiffness is obtained by an inverse vibration analysis and deflection method. The details of the two methods are given. The results by the two methods are presented graphically and show good agreement. Crack locations are also determined by the inverse analysis. The maximum absolute error in the location is 13.80%. Experimentally determined variation of rotational spring stiffness with ratio of crack size to thickness is utilized to predict the crack sizes. The maximum absolute errors in prediction of crack size are 17.24% and 16.90% for aluminium and mild steel pipes respectively.

Keywords

References

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