Lamb mode spectra versus the Poisson ratio in a free isotropic elastic plate
Résumé
The variation, with material parameters, of Lamb modes is investigated. Vibration spectra of traction-free elastic plates are generally presented, for a given isotropic material, as a set of dispersion curves corresponding to the various Lamb mode branches. Here, the spectrum variations, with the Poisson ratio , are plotted in a dimensionless coordinate system in the form of a bundle of curves for each Lamb mode. Except for the fundamental anti-symmetric mode A 0 , this representation highlights the same behavior for all Lamb modes. V T denoting the shear wave velocity, the ͑ , k͒ plane can be divided into two angular sectors separated by the line of slope V T ͱ 2. In the upper one, corresponding to a phase velocity V = / k larger than V T ͱ 2, dispersion curves are very sensitive to the plate material parameters. In the lower sector ͑V Ͻ V T ͱ 2͒ all the branches, whatever the value of the Poisson ratio ͑0 Յ Ͻ 0.5͒, are gathered into a thin pencil. Moreover, curves of a given bundle cross the boundary line at coincidence points equally spaced. These properties and a specific behavior observed for = 0 are explained in terms of Lamé wave solutions of the characteristic equations of Lamb modes.
Domaines
Physique [physics]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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