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首页> 外文会议>NATO Advanced Research Workshop on Surface Waves in Anisotropic and Laminated Bodies and Defects Detection; 20011030-1102; Moscow(RU) >NONLINEARITY IN ELASTIC SURFACE WAVES ACTS NONLOCALLY
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NONLINEARITY IN ELASTIC SURFACE WAVES ACTS NONLOCALLY

机译：弹性表面中的非线性非局部性

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摘要

Since elastic surface waves are examples of guided waves, nonlinear effects are significant only between linearized modes which have good matching of both phase and group velocities. Within homogeneous half-spaces, linearized modes travelling across the surface in any direction are completely non-dispersive. The phase speed can depend upon direction, but not upon frequency (or wavelength). Consequently, the standard weakly nonlinear theory equates the derivative of the (complex) Fourier transform of the surface displacement to an integral of convolution type, with a kernel which involves various elastic moduli and which takes account of the depth-dependence of the displacement fields within interacting pairs of modes having any two distinct wavenumbers. The direct formulation of the equation governing the evolution of surface slope involves a quadratically nonlinear, nonlocal operator, incorporating the fact that waveform evolution is influenced by quadratically nonlinear contributions to the stress at all depths. This kernel splits naturally into one entirely local part, a nonlocal part allowing wave profiles to preserve symmetry and one necessarily causing asymmetry. Details are determined for elastic materials of arbitrary anisotropy.
机译：由于弹性表面波是导波的示例，因此非线性效应仅在线性模式之间具有显着的效果，而线性模式具有相位和群速度的良好匹配。在均匀的半空间内，沿任何方向在表面上传播的线性化模式是完全非分散的。相速度可以取决于方向，而不取决于频率（或波长）。因此，标准的弱非线性理论将表面位移的（复杂）傅立叶变换的导数等同于卷积类型的积分，其内核涉及各种弹性模量，并考虑了位移场在其中的深度依赖性。具有任何两个不同波数的相互作用模式对。控制表面坡度演化的方程式的直接公式涉及二次非线性的非局部算子，并结合了这样一个事实，即波形的演化受二次非线性对所有深度应力的影响。该内核自然地分裂成一个完全局部的部分，一个非局部的部分允许波轮廓保持对称性，而这必然导致不对称性。确定具有任意各向异性的弹性材料的细节。

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