Abstract
Lamb waves exhibit conical dispersion at zero wave number when an accidental degeneracy occurs between thickness mode longitudinal and shear resonances of the same symmetry. Here we investigate the propagation of Lamb waves generated at the conical point frequency and the interaction of these waves with defects and interfaces. The group velocity and mode shapes of Lamb waves at the conical point are found, and it is shown that as the wavenumber gets close to zero, considerable group velocity is seen only for material properties supporting a degeneracy or near-degeneracy. The unusual wave propagation and mode conversion of Lamb waves generated at the conical point are elucidated through numerical simulations. Experimental measurements of near conical point Lamb wave interaction with holes in a plate demonstrate that these waves flow around defects while maintaining a constant phase of oscillation across that plate surface.
Highlights
Background and TheoryConical dispersion: group velocity and mode shape
We have studied the propagation of conical point and near-conical point Lamb waves in an isotropic plate and the interaction of these waves with plate boundaries and interfaces
By calculating the group velocity of long wavelength Lamb waves as a function of Poisson’s ratio, we show that Lamb waves with non-negligible group velocities close to k = 0 exist only near degeneracies between thickness mode longitudinal and shear resonances of the same symmetry
Summary
A source exciting waves at the conical point produces a spatially uniform oscillation that spreads or flows over the plate surface and is insensitive to wavelength dependent wave phenomena such as diffraction and scattering. The conical www.nature.com/scientificreports point wave produces a spatially uniform oscillation of the plate surface that shows little evidence of perturbation by the hole.
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