Intersections of the Lamb mode dispersion curves of free isotropic plates.
The intersections between Lamb mode dispersion curves of free isotropic plates at real values of frequency and wave number are examined for the full allowed range of Poisson's ratio σ. The generic intersections between the dispersion curves for symmetric and anti-symmetric branches are classified into three types. Type F intersections are conditioned by the two additional real solutions of Rayleigh's cubic equation that occur for σ<0.26308. Types I and II intersections occur for all values of σ, and are distinguished by the vanishing or divergence of the tangent functions in the defining equations for the Lamb modes. A brief discussion is provided of intersections between branches of like symmetry and additional intersections between unlike symmetry branches that occur for special values of σ.
School of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa.
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