Crossings of Lamb modes in lead zinc niobate-lead titanate crystal plates

Abstract

Frequency dispersions of Lamb waves in [001]c and [011]c polarized lead zinc niobate-lead titanate crystal free infinite plates are studied based on the partial wave theory. Multiple crossings between symmetric and antisymmetric Lamb modes are found only in [001]c polarized crystals, and most of the dispersion relations would exhibit the same rule as that in lead magnesium niobate-lead titanate crystals. It is found that multiple crossings between A0 and S0 modes are directly related to the multivalued quasishear vertical slowness curves. A pair of complex conjugate roots of the wave number in the x3 direction is found in a certain area. Equation of elastic constants is obtained when A0 and S0 modes cross under this condition, which can be conveniently used to judge whether A0 and S0 modes cross for crystals with orthogonal and tetragonal symmetries.