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Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation.

Evripides Georgiades1, Michael J S Lowe1, Richard V Craster1,2

  • 1Department of Mechanical Engineering, Imperial College London, London SW7 1AY, United Kingdom.

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Summary
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A new spectral collocation method accurately computes complex leaky waves in elastic waveguides, overcoming numerical challenges for non-destructive evaluation. This advance enhances guided wave inspection capabilities.

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Area of Science:

  • Acoustics
  • Materials Science
  • Computational Mechanics

Background:

  • Guided wave inspections in non-destructive evaluation involve elastic structures embedded in other media.
  • Calculating leaky waves in such systems is complex due to non-trivial wave propagation and numerical challenges.
  • Existing methods struggle with the exponential amplitude growth of leaky waves in surrounding media.

Purpose of the Study:

  • To develop an accurate and efficient numerical method for identifying leaky wave modes in elastic waveguides.
  • To address the challenges posed by complex wavenumber solutions in leaky wave computation.
  • To enable reliable analysis of guided wave propagation in embedded elastic structures.

Main Methods:

  • A spectral collocation method was employed to discretize elastic domains.
  • Complex paths were mapped using domain discretization, tailored to exterior bulk wavespeeds, ensuring numerical decay and physical preservation.
  • The method iterated through all radiation cases to retrieve dispersion and attenuation curves.

Main Results:

  • The spectral collocation method accurately identified leaky wave modes propagating into elastic half-spaces.
  • Full sets of dispersion and attenuation curves were successfully retrieved.
  • Results were validated against the commercial software 'Disperse' and finite element simulations.

Conclusions:

  • The presented spectral collocation method offers an accurate and efficient solution for computing leaky waves in complex elastic systems.
  • This method overcomes limitations of existing numerical techniques, particularly regarding amplitude growth in surrounding media.
  • The findings are crucial for advancing non-destructive evaluation techniques using guided waves in embedded structures.