Pipe crack identification based on finite element method of second generation wavelets

In this paper, a new method is presented to identify crack location and size, which is based on stress intensity factor suitable for pipe structure and finite element method of second generation wavelets (SGW-FEM). Pipe structure is dispersed into a series of nested thin-walled pipes. By making use of stress intensity factor of the thin-walled pipe, a new calculation method of crack equivalent stiffness is proposed to solve the stress intensity factor of the pipe structure. On this basis, finite element method of second generation wavelets is used to establish the dynamic model of cracked pipe. Then we combine forward problem with inverse problem in order to establish quantitative identification method of the crack based on frequency change, which provides a non-destructive testing technology with vibration for the pipe structure. The efficiency of the proposed method is verified by experiments.

[1]  S. K. Maiti,et al.  On prediction of crack in different orientations in pipe using frequency based approach , 2008 .

[2]  S. Chinchalkar DETERMINATION OF CRACK LOCATION IN BEAMS USING NATURAL FREQUENCIES , 2001 .

[3]  S. P. Lele,et al.  Modelling of Transverse Vibration of Short Beams for Crack Detection and Measurement of Crack Extension , 2002 .

[4]  Andrew D. Dimarogonas,et al.  VIBRATION OF CRACKED SHAFTS IN BENDING , 1983 .

[5]  Zhengjia He,et al.  Adaptive multiresolution finite element method based on second generation wavelets , 2007 .

[6]  Kevin Amaratunga,et al.  Generalized hierarchical bases: a Wavelet‐Ritz‐Galerkin framework for Lagrangian FEM , 2005 .

[7]  Zhengjia He,et al.  The construction of plane elastomechanics and Mindlin plate elements of B-spline wavelet on the interval , 2006 .

[8]  Kevin Amaratunga,et al.  Spatially Adapted Multiwavelets and Sparse Representation of Integral Equations on General Geometries , 2002, SIAM J. Sci. Comput..

[9]  Robert D. Adams,et al.  A Vibration Technique for Non-Destructively Assessing the Integrity of Structures: , 1978 .

[10]  Oleg V. Vasilyev,et al.  Second-generation wavelet collocation method for the solution of partial differential equations , 2000 .

[11]  W. Sweldens The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[12]  Kevin Amaratunga,et al.  A multiresolution finite element method using second generation Hermite multiwavelets , 2003 .

[13]  W. Sweldens Wavelets and Their Applications, M. B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael, Eds., Jones and Bartlett, 1992, xiii + 474 pp. , 1993 .

[14]  Jean-Michel Poggi,et al.  Wavelets and their applications , 2007 .

[15]  Hiroshi Tada,et al.  The stress analysis of cracks handbook , 2000 .

[16]  Bing Li,et al.  A dynamic multiscale lifting computation method using Daubechies wavelet , 2006 .

[17]  Wim Sweldens,et al.  Building your own wavelets at home , 2000 .

[18]  Zhengjia He,et al.  Identification of crack in a rotor system based on wavelet finite element method , 2007 .

[19]  Richard M. Beam,et al.  Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets , 2000, SIAM J. Sci. Comput..

[20]  Amir Reza Shahani,et al.  Finite element analysis of dynamic crack propagation using remeshing technique , 2009 .

[21]  Zhengjia He,et al.  The construction of wavelet finite element and its application , 2004 .