Sensor requirements for in situ imaging of multiple damage by Lamb waves

Lamb waves are guided waves that propagate in plate-like structures. These waves are well suited for wide-area inspection, such as aircraft wing skins, because of their relatively slow geometrical decay with propagation distance. Recently, a computationally efficient algorithm for in situ imaging was derived based on the multi-static data matrix. Here, previous work on imaging a single circular inhomogeneity is extended to the case of structural damage spread over two distinct sites. Detailed results are presented for the rank and bandwidth of the data matrix, showing the dependence on the overall size of the damage cluster. The implications of these results for the practically important problem of determining minimum sensor requirements for image reconstruction are discussed. References C. T. Ng and M. Veidt. A Lamb-wave-based technique for damage detection in composite laminates. Smart Mater. Struct., 18(7):074006, 2009. doi:10.1088/0964-1726/18/7/074006 J. E. Michaels and T. E. Michaels. Guided wave signal processing and image fusion for in situ damage localization in plates. Wave Motion, 44(6):482–192, 2007. doi:10.1016/j.wavemoti.2007.02.008 J. S. Hall and J. E. Michaels. Multi-path guided wave imaging for in situ monitoring of complex structures. AIP Conf. Proc. 1511:707-713, 2013. doi:10.1063/1.4789115 Z. Q. Su, L. Cheng, X. M. Wang and L. Yu. Diagnostic imaging for structural damage. Adv. Mater. Res., 47–50:1157–1160, 2008. doi:10.4028/www.scientific.net/AMR.47-50.1157 L. R. F. Rose and C. H. Wang. Mindlin plate theory for damage detection: Source solutions. J. Acoust. Soc. Am., 116(1):154–171, 2004. doi:10.1121/1.1739482 L. R. F. Rose and C. H. Wang. Mindlin plate theory for damage detection: Imaging of flexural inhomogeneities. J. Acoust. Soc. Am., 127(2):754–763, 2010. doi:10.1121/1.3277217 C. H. Wang and L. R. F. Rose. Imaging damage using Mixed Passive and Active Sensors. 4th Asia-Pacific Workshop on Structural Health Monitoring, 2012, Melbourne, Australia. C. H. Wang and L. R. F. Rose. Minimum Sensor Density for Quantitative Damage Imaging. 9th International Workshop on Structural Health Monitoring, 2013, Standford, USA. E. Chan, C. H. Wang and L. R. F. Rose. Characterisation of Part-through Damage in a Stiffened Panel by a Time-reversal Based Imaging Method. 9th International Workshop on Structural Health Monitoring, 2013, Standford, USA. Abaqus/Explicit 6.10 Dassault Systemes http://www.3ds.com/products-services/simulia/portfolio/abaqus/abaqus-portfolio/abaqusexplicit