分层半空间表面非线性瑞利波的激发*

针对非线性瑞利波在均匀分层半空间结构中的激发和传播规律进行研究。根据摄动理论和模态分解将分层半空间结构中瑞利波的二次谐波声场表示为二倍频瑞利波模式的线性组合，经由互易关系得到各模式的展开系数表达式。对不同分层半空间结构中瑞利波二次谐波的激发和传播特性进行讨论，结果表明相速度匹配的瑞利波模式其二次谐波分量随传播距离线性增长，非匹配模式的二次谐波分量则沿传播方向周期震荡传播。此外，文中定义非线性参数表征瑞利波模式产生的非线性程度，这有利于选择出具有明显非线性效应的匹配点，为后续检测工作提供理论依据，具有指导意义。

Excitation of nonlinear Rayleigh waves on a layered half-space surface*

The excitation and propagation laws of nonlinear Rayleigh waves in a homogeneous layered half-space are studied in this paper. The second harmonic of Rayleigh waves in the layered half-space model is written as a linear combination of Rayleigh-wave modes by using the perturbation technique and the modal decomposition, then the second-order modal amplitudes are obtained via a reciprocity relation. The excitation and propagation laws of nonlinear Rayleigh waves are discussed in various layered half-spaces. The results show that the phase-matched double-frequency mode grows at a linear rate with propagation distance, while other double-frequency modes oscillate with the propagation distance. Besides, the nonlinear parameter defined in this work is not only beneficial to select matching points with obvious nonlinear effects, but also provides a theory for practical nonlinear Rayleigh wave detection.