Abstract We propose a numerical approach for the calculation of frequency–dispersion curves in a flat anisotropic waveguide based on the Ritz–Rayleigh method, offering several significant benefits over commonly used analytical and numerical models. The problem is linearized using a tailored functional basis based on Legendre polynomials, utilizing all symmetries provided by the problem to reduce the computational demands, which brings significant benefits for an inverse procedure, and thus for material characterization. The approach is completely general in terms of elastic properties and direction of propagation. As an exemplary calculation, frequency–dispersion curves of phase and group velocity are calculated for a (001)-oriented free-standing film of the Ni–Mn–Ga alloy exhibiting a strong cubic anisotropy. In the case of propagation along the [100] direction, the dispersion curves oscillate strongly, creating pairs of symmetric and antisymmetric modes. Taking advantage of the generality of the approach, the curves are also presented for the case of extreme anisotropy. Sets of curves for directions [110] and [1 0.9 0] (i.e., 3 ∘ off [110]), where the pseudo-surface wave exists, are also calculated. High-frequency asymptotes are shown to correspond with surface and bulk modes propagating along the plate.

中文翻译：

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Litz-Rayleigh 方法在极端各向异性介质中的兰姆波应用

摘要 我们提出了一种基于 Ritz-Rayleigh 方法计算平面各向异性波导中频率-色散曲线的数值方法，与常用的分析和数值模型相比，该方法具有几个显着的优点。该问题使用基于勒让德多项式的定制函数基础进行线性化，利用问题提供的所有对称性来减少计算需求，这为逆过程带来了显着的好处，从而为材料表征带来了好处。该方法在弹性特性和传播方向方面是完全通用的。作为示例性计算，计算了表现出强立方各向异性的 Ni-Mn-Ga 合金的 (001) 取向自支撑膜的相位和群速度的频率-色散曲线。在沿 [100] 方向传播的情况下，色散曲线强烈振荡，产生对称和反对称模式对。利用该方法的一般性，还针对极端各向异性的情况提供了曲线。还计算了存在伪表面波的方向 [110] 和 [1 0.9 0]（即 3 ∘ off [110]）的曲线集。高频渐近线与沿板传播的表面和体模相对应。也计算。高频渐近线与沿板传播的表面和体模相对应。也计算。高频渐近线与沿板传播的表面和体模相对应。