High sensibility imaging of defects in elastic waveguides using near resonance frequencies

Angèle Niclas (1, 2, 3) , Eric Bonnetier (4, 5) , L. Seppecher (6, 7) , Grégory Vial (7, 6)

1 X - École polytechnique
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 IP Paris - Institut Polytechnique de Paris
4 IF - Institut Fourier
5 UGA - Université Grenoble Alpes
6 ECL - École Centrale de Lyon
7 ICJ - Institut Camille Jordan

This work presents a new multi-frequency inversion method to image shape defects in slowly varying elastic waveguides. Contrary to previous works in this field, we choose to take advantage of the near resonance frequencies of the waveguide, where the elastic problem is known to be ill-conditioned. A phenomenon close to the tunnel effect in quantum mechanics can be observed at these frequencies, and locally resonant modes propagate in the waveguide. These modes are very sensitive to width variations, and measuring their amplitude enables reconstructing the local variations of the waveguide shape with very high sensibility. Given surface wavefield measurements for a range of near resonance frequencies, we provide a stable numerical reconstruction of the width of a slowly varying waveguide and illustrate it on defects like dilation or compression of a waveguide.

Mots clés: Waveguide; Inverse problems; Resonances

Domaines: Analyse numérique [math.NA]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Angèle Niclas, Eric Bonnetier, L. Seppecher, Grégory Vial. High sensibility imaging of defects in elastic waveguides using near resonance frequencies. WAVES Conference, Jul 2022, Palaiseau, France. ⟨hal-03861288⟩