A model-based approach to dispersion and parameter estimation for ultrasonic guided wavesThe propagation of Lamb waves in a plate with an engraved periodic grating is addressed in this article. Mode conversions and reflections are analyzed. In the first part the conversion modes are explained by the existence of a resonance condition between the Lamb-wave wavenumbers and the fundamental and harmonic spatial periods of the grating. These phenomena are experimentally and numerically highlighted for a metallic waveguide with a rectangular grating. The second part focuses on the pseudo-Lamb wave dispersion curves in a periodic waveguide. The periodicity implies that the Lamb waves dispersion curves fold back at the edge of the Brillouin zone. Several stop bands appear: classical band gaps at the boundary of the Brillouin zone and mini-stop-bands inside the Brillouin zone. For the ministop band, dispersion curves cross and a possible coupling occurs between the modes. Finally, conversions or the existence of gaps are linked with the Power Spectral Density of the grating profile.
The study of the normal diffusion of an ultrasonic plane wave by cylinders and plates imbedded in the water shows resonances which are the natural modes of vibration. When a natural mode of an elastic target is excited, the energy which is stored during the forced excitation is emitted after the end of the forced excitation. The observation of backscattered spectra obtained by the Resonance Isolation and Identification Method (RIIM) from an aluminum cylinder shows supplementary resonances. The directivity pattern of the transducer is the cause of these supplementary resonances. The behavior of these resonances is analogous to the resonances of the plate. This leads us to study the natural modes of the cylinder. All the resonances which are experimentally detected may be considered as normal modes of the target. The results obtained on plates and cylinders have a common point: the generation of a guided wave by the excitation of a resonance.
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