Analytical solutions for crack-like scatterers and sources in isotropic elastic plates

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A common theoretical framework can be employed for modelling both active and passive approaches to structural health monitoring based on guided waves. The same fundamental solutions can be used to represent the scattered field due to crack-like damage in an active approach, or the acoustic emission due to various failure mechanisms in a passive approach. It is shown that the reciprocal theorem can be used to derive compact analytical formulae for those fundamental solutions expressed as sums over the propagating modes. The only detailed calculations that are required are those involved in determining the relevant dispersion curves and through-thickness mode functions. For clarity, the approach is first described for two-dimensional configurations. The subsequent extension to three-dimensional requires the stationary phase approximation. It is shown that the modal coefficients for crack-like sources (or scatterers) are proportional to the conjugate stress component of the corresponding mode. Furthermore, the approach can also be used for an edge crack or delamination in a semi-infinite plate, and the theoretical formulae are compared with experimentally validated computational results for that case. Further extensions are briefly noted.

Original languageEnglish
Article number102476
Number of pages20
JournalWave Motion
Publication statusPublished - Jan 2020


  • Edge crack scattering
  • Elastodynamics
  • Equivalent body forces
  • Lamb waves
  • Point-like source
  • Reciprocal theorem

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