铌锌酸铅-钛酸铅薄层中Lamb波模式的交叉特性

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

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A_0和S_0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x_3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A_0和S_0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A_0和S_0模式是否交叉提供了一种直观、简便的方法.

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 Ao and So modes are directly related to the multivalued quasishear vertical slowness curves. A pair of complex conjugate roots of the wave number in the χ3 direction is found in a certain area. Equation of elastic constants is obtained when Ao and So modes cross under this condition, which can be conveniently used to judge whether Ao and So modes cross for crystals with orthogonal and tetragonal symmetries.