铌锌酸铅-钛酸铅薄层中Lamb波模式的交叉特性

以[001]_c和[011]_c极化的铌锌酸铅-钛酸铅晶体为研究对象, 利用子波理论对其无限大自由薄层中传播的Lamb波的色散及模式交叉特性进行了研究. 发现只有[001]_c极化的晶体中的对称与反对称模式Lamb波之间出现了多次交叉, 并且变化规律与铌镁酸铅-钛酸铅的情形相同. Lamb波的A₀和S₀模式的交叉是由准纵向剪切波慢度曲线的多值关系引起的, 此时其x₃方向的波数在一定范围内存在一对非纯虚数的复共轭根. 利用此结论推导出A₀和S₀模式交叉时弹性常数需要满足的条件, 为判断正交、四方对称性晶体中Lamb波的A₀和S₀模式是否交叉提供了一种直观、简便的方法.

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

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.