Modelling, detection and identification of flexural crack damages in beams using frequency response functions

Abstract In this paper, the original receptance method first proposed by Bishop (The mechanics of vibration. Cambridge University Press, Cambridge, 1979) is further generalized and extended to the vibration modelling of stepped beams and truss structures with multiple crack damages. Cracks are physically treated as rotational springs representing local flexibilities at crack locations induced by crack depths. Frequency response functions (FRFs) with any given number of crack locations and depths are first established from which numerically exact natural frequencies and mode shapes are extracted. Since these FRFs can be measured in practice in a typical modal testing, a crack location method is then developed by using rotational FRFs which can be estimated from these measured translational FRF data. Substantial slope discontinuities are observed and are further employed to construct a crack location matrix to locate cracks. Finally, to identify crack parameters such as crack depths, a new Numerical Inverse FRF Sensitivity method is developed. Unlike the case of analytical model updating where an analytical model is available from which sensitivities can be derived, FRF sensitivities needed in this case have to be numerically computed. Such numerical sensitivity approach is believed to have wider applications in inverse dynamics problems such as analytical model updating. A stepped beam and a GARTEUR structure are employed in numerical case studies and very encouraging results have been achieved even when FRF data are contaminated with substantial measurement noise.

[1]  G. Irwin.  ANALYSIS OF STRESS AND STRAINS NEAR THE END OF A CRACK TRAVERSING A PLATE , 1957 .

[2]  H. Liebowitz,et al.  Carrying capacity of notched columns , 1967 .

[3]  L. Freund,et al.  Dynamic Fracture of a Beam or Plate in Plane Bending , 1976 .

[4]  Nikos A. Aspragathos,et al.  Identification of crack location and magnitude in a cantilever beam from the vibration modes , 1990 .

[5]  W. Ostachowicz,et al.  Analysis of the effect of cracks on the natural frequencies of a cantilever beam , 1991 .

[6]  R. Gasch,et al.  A Survey Of The Dynamic Behaviour Of A Simple Rotating Shaft With A Transverse Crack , 1993 .

[7]  D. Ewins,et al.  Analytical model improvement using frequency response functions , 1994 .

[8]  H. Du,et al.  Improved Inverse Eigensensitivity Method for Structural Analytical Model Updating , 1995 .

[9]  Y. Narkis,et al.  Crack identification in a cantilever beam under uncertain end conditions , 1996 .

[10]  Andrew D. Dimarogonas,et al.  Vibration of cracked structures: A state of the art review , 1996 .

[11]  M. K. Lim,et al.  Relationship Between Improved Inverse Eigensensitivity and FRF Sensitivity Methods for Analytical Model Updating , 1997 .

[12]  Thomas G. Chondros,et al.  The continuous crack flexibility model for crack identification , 2001 .

[13]  J. Fernández-Sáez,et al.  FUNDAMENTAL FREQUENCY OF CRACKED BEAMS IN BENDING VIBRATIONS: AN ANALYTICAL APPROACH , 2002 .

[14]  G. Owolabi,et al.  Crack detection in beams using changes in frequencies and amplitudes of frequency response functions , 2003 .

[15]  R. Lin,et al.  Frequency selection method for FRF-based model updating , 2004 .

[16]  Rongming Lin,et al.  Model updating of damped structures using FRF data , 2006 .

[17]  S. A. Billings,et al.  Crack detection using nonlinear output frequency response functions - an experimental study , 2006 .

[18]  Jean-Jacques Sinou,et al.  Robust damage assessment of multiple cracks based on the Frequency Response Function and the Constitutive Relation Error updating method , 2008 .

[19]  S. S. Law,et al.  Dynamic condition assessment of a cracked beam with the composite element model , 2009 .

[20]  R. Perera,et al.  Structural crack detection without updated baseline model by single and multiobjective optimization , 2009 .

[21]  Marta B. Rosales,et al.  Crack detection in beam-like structures , 2009 .

[22]  S. Caddemi,et al.  Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks , 2009 .

[23]  Animesh Chatterjee,et al.  Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions , 2010 .

[24]  Rajiv Tiwari,et al.  Identification of a multi-crack in a shaft system using transverse frequency response functions , 2010 .

[25]  Paolo Pennacchi,et al.  A sensitivity analysis of vibrations in cracked turbogenerator units versus crack position and depth , 2010 .

[26]  Zhengjia He,et al.  Pipe crack identification based on finite element method of second generation wavelets , 2010 .

[27]  Fernando Cruz-Peragón,et al.  A methodology for cracks identification in large crankshafts , 2011 .

[28]  S. Oyadiji,et al.  Crack detection in simply supported beams using stationary wavelet transform of modal data , 2011 .

[29]  Fulei Chu,et al.  Local flexibility of an elliptical cracked shaft under bending and tension , 2011 .

[30]  Hui Li,et al.  Application of Hermitian wavelet to crack fault detection in gearbox , 2011 .

[31]  R. Bishop,et al.  The Mechanics of Vibration , 2011 .

[32]  Itzhak Green,et al.  Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results , 2012 .

[33]  U. Andreaus,et al.  Experimental damage detection of cracked beams by using nonlinear characteristics of forced response , 2012 .

[34]  M. Attar.  A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions , 2012 .

[35]  S. Caddemi,et al.  The exact explicit dynamic stiffness matrix of multi-cracked Euler–Bernoulli beam and applications to damaged frame structures , 2013 .

[36]  J. Sinha,et al.  Development of residual operational deflection shape for crack detection in structures , 2014 .

[37]  A. Karrech,et al.  Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model , 2014 .

[38]  W. Ostachowicz,et al.  Identification of cracks in thin-walled structures by means of wavenumber filtering , 2015 .