By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.

中文翻译：

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基于应变梯度弹性理论的涂层半空间面内表面波传播

通过采用应变梯度弹性理论，我们研究了具有微结构的涂层半空间中面内表面波的传播。我们首先研究当前问题的一般情况，即表面层和半空间均由应变梯度弹性理论描述。我们制定了一般情况的边界和连续性条件，并推导了表面波的色散关系。然后我们研究了两种特殊情况：（1）表面层用应变梯度弹性理论描述，而半空间用经典弹性理论描述；(2)表层采用经典弹性理论描述，半空间采用应变梯度弹性理论描述。我们研究了所有情况下应变梯度特征长度对表面波色散曲线的影响。这项研究有助于进一步了解弹性波在具有微结构的材料中的传播特性。