Analysis of mode conversion and scattering of guided waves at cracks in isotropic beams using a time-domain spectral finite element method

Detecting damages in its early stage, and hence, to ensure the safety and reliability of structures is of vital important. Guided waves have been recognised as one of the promising damage detection techniques that are sensitive to small and different types of damages. The understanding of guided wave propagation and scattering phenomena at the damages is one of the fundamental elements to facilitate the development of this technique for damage characterisation. This paper presents a study of scattering characteristics and mode conversion effects of guided waves at cracks in isotropic beams. An efficient time-domain spectral finite element method using one-dimensional (1D) beam element is developed to solve this problem. The developed model is then used to carry out a series of case studies that consider different crack sizes in the beams. These parametric studies provide a fundamental physical insight into the mode conversion phenomena and scattering characteristics of the guided waves at the cracks.

[1]  Hoon Sohn,et al.  A Review of Structural Health Review of Structural Health Monitoring Literature 1996-2001. , 2002 .

[2]  Srinivasan Gopalakrishnan,et al.  Wave propagation in stiffened structures using spectrally formulated finite element , 2013 .

[3]  James C. Newman,et al.  An empirical stress-intensity factor equation for the surface crack , 1981 .

[4]  Laurence J. Jacobs,et al.  Modeling elastic wave propagation in waveguides with the finite element method , 1999 .

[5]  W. Witkowski,et al.  Damage Detection of A T-Shaped Panel by Wave Propagation Analysis in the Plane Stress / Wykrywanie Uszkodzen W Tarczy Typu T Z Uzyciem Analizy Propagacji Fal W Płaskim Stanie Naprezenia , 2012 .

[6]  Ching-Tai Ng,et al.  Bayesian model updating approach for experimental identification of damage in beams using guided waves , 2014 .

[7]  Pizhong Qiao,et al.  Vibration-based Damage Identification Methods: A Review and Comparative Study , 2011 .

[8]  C. Ng,et al.  Scattering of the fundamental anti-symmetric Lamb wave at delaminations in composite laminates. , 2011, The Journal of the Acoustical Society of America.

[9]  WJ Zhou,et al.  Wave scattering by local defect in structural waveguide through wave finite element method , 2011 .

[10]  C. Pozrikidis,et al.  Introduction to finite and spectral element methods using MATLAB , 2014 .

[11]  Joseph L. Rose,et al.  A Baseline and Vision of Ultrasonic Guided Wave Inspection Potential , 2002 .

[12]  Carlos E. S. Cesnik,et al.  Review of guided-wave structural health monitoring , 2007 .

[13]  Guang Meng,et al.  Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method , 2012 .

[14]  E. Peter Carden,et al.  Vibration Based Condition Monitoring: A Review , 2004 .

[15]  J. Jensen On the shear coefficient in Timoshenko's beam theory , 1983 .

[16]  Fabio Biondini,et al.  Finite strip modeling for optimal design of prestressed folded plate structures , 2004 .

[17]  G. Cowper The Shear Coefficient in Timoshenko’s Beam Theory , 1966 .

[18]  Magdalena Rucka,et al.  Experimental and numerical study on damage detection in an L-joint using guided wave propagation , 2010 .

[19]  L. Rose,et al.  Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates , 2012 .

[20]  Zhiquan He,et al.  Lamb wave mode conversion-based crack detection for plate-like structures without baseline information , 2013 .

[21]  Michel Castaings,et al.  Modal decomposition method for modeling the interaction of Lamb waves with cracks. , 2002, The Journal of the Acoustical Society of America.

[22]  B. P. Deepak,et al.  Dynamics of rotating composite beams: A comparative study between CNT reinforced polymer composite beams and laminated composite beams using spectral finite elements , 2012 .

[23]  J. W. Hutchinsonb,et al.  Surface crack subject to mixed mode loading , 2022 .

[24]  Maciej Radzieński,et al.  Structural health monitoring by means of elastic wave propagation , 2012 .

[25]  P. Cawley,et al.  The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave a0 from a rectangular notch in a plate. , 2002, The Journal of the Acoustical Society of America.

[26]  Christ Glorieux,et al.  Lamb mode conversion in a plate with a delamination , 2004 .

[27]  The shear coefficient for quartz crystal of rectangular cross section in Timoshenko's beam theory , 1996, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[28]  Wei Hong,et al.  Finite-difference frequency-domain algorithm for modeling guided-wave properties of substrate integrated waveguide , 2003 .

[29]  J. Rose Ultrasonic Waves in Solid Media , 1999 .

[30]  J. Rose,et al.  Boundary element modeling for defect characterization potential in a wave guide , 2003 .

[31]  Marek Krawczuk,et al.  Spectral Finite Element Method , 2012 .

[32]  Weiqi Wang,et al.  Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch. , 2014, Ultrasonics.

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

[34]  Sai T. Chu,et al.  A finite-difference time-domain method for the design and analysis of guided-wave optical structures , 1989 .

[35]  Martin Veidt,et al.  Guided wave damage characterisation in beams utilising probabilistic optimisation , 2009 .

[36]  Li Cheng,et al.  Nonlinear Properties of Lamb Waves under Modulation of Fatigue Damage: Finite Element Simulation with Experimental Validation , 2013 .

[37]  M. Veidt,et al.  Single Transducer Pair Lamb Wave Time Reversal for Damage Detection in Composite Laminates , 2013 .

[38]  Raymond D. Mindlin,et al.  A One-Dimensional Theory of Compressional Waves in an Elastic Rod , 1989 .

[39]  Gui-Rong Liu A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates , 2002 .

[40]  Guido De Roeck,et al.  Vibration-based damage identification: the Z24 benchmark , 2014 .

[41]  Martin Veidt,et al.  Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric Lamb wave at through holes in composite laminates. , 2011, The Journal of the Acoustical Society of America.

[42]  Emmanuel Moulin,et al.  Study of the fundamental Lamb modes interaction with symmetrical notches , 2008 .

[43]  Anoop Chawla,et al.  Coupled bending, longitudinal and torsional vibrations of a cracked rotor , 2004 .