Dispersion of Rayleigh waves in weakly anisotropic media with vertically-inhomogeneous initial stress
Dispersion of Rayleigh waves in weakly anisotropic media with vertically-inhomogeneous initial stress
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DOI：
10.1016/j.ijengsci.2015.03.001
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发表时间：
2015-07
影响因子：
6.6
通讯作者：
Kazumi Tanuma;C. Man;Yuewei Chen
中科院分区：
文献类型：
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作者：
Kazumi Tanuma;C. Man;Yuewei Chen
在这里，我们提出了一个程序，通过该程序可以导出瑞利波的频散关系，沿沿着自由表面的垂直不均匀，预应力，一般各向异性半空间的各个方向传播。该过程基于三个假设，即：（i）材料半空间的增量弹性张量可以写为均匀各向同性部分C Iso和与深度相关的扰动部分A的和;（ii）在自由表面处，初始应力和A都小于C Iso;（iii）质量密度、初始应力和A是自由表面深度的光滑函数。我们推导出公式和Lyapunov型方程，可以迭代地提供表面阻抗矩阵的渐近展开的每个项，这导致前面提到的瑞利波色散的高频渐近公式。作为示例，我们考虑AA 7075-T651铝合金的厚板样品，其具有通过低塑性抛光处理的一个面，该抛光在处理表面处和紧邻处理表面之下诱导（深度依赖性）预应力。我们建模的样品作为一个预应力，弱纹理的正交晶系聚集体的立方微晶和工作明确，到第三阶，色散关系，涉及到瑞利波传播在几个方向沿着处理面的样品。
Herein we present a procedure by which a high-frequency asymptotic formula can be derived for dispersion relations of Rayleigh waves that propagate in various directions along the free surface of a vertically-inhomogeneous, prestressed, and generally anisotropic half-space. The procedure is based on three assumptions, namely:(i) the incremental elasticity tensor of the material half-space can be written as the sum of a homogeneous isotropic part C Iso and a depth-dependent perturbative part A;(ii) at the free surface both the initial stress and A are small as compared with C Iso;(iii) the mass density, the initial stress, and A are smooth functions of depth from the free surface. We derive formulas and Lyapunov-type equations that can iteratively deliver each term of an asymptotic expansion of the surface impedance matrix, which leads to the aforementioned high-frequency asymptotic formula for Rayleigh-wave dispersion. As illustration we consider a thick-plate sample of AA 7075-T651 aluminum alloy, which has one face treated by low plasticity burnishing that induced a (depth-dependent) prestress at and immediately beneath the treated surface. We model the sample as a prestressed, weakly-textured orthorhombic aggregate of cubic crystallites and work out explicitly, up to the third order, the dispersion relations that pertain to Rayleigh waves propagating in several directions along the treated face of the sample.