Abstract The response features of second-harmonic generation (SHG) of primary Lamb wave propagation to the thickness of microdamage layer (MDL) in a solid plate have been theoretically and numerically investigated in this paper. Here the solid plate with a MDL is regarded as a double-layered plate in analysis of nonlinear Lamb wave propagation. On the basis of a second-order perturbation approximation and modal expansion analysis, the physical process of cumulative SHG by primary Lamb wave propagation in a solid plate with a MDL has been investigated. The influence of variation in the thickness of MDL on the effect of SHG of primary S 0 mode, which satisfies an approximate phase velocity matching in the low frequency region, has been theoretically analyzed, and then the finite element (FE) simulation has been carried out to validate the results of the theoretical predictions. A close agreement between the theoretical analyses and FE simulations validates the effectiveness of using the effect of SHG of primary S 0 mode for characterizing changes in the thickness of MDL. Moreover, change mechanism of nonlinear acoustic parameter with the thickness of MDL is revealed It is expected that the results obtained can provide a convenient means for accurately characterizing nonhomogeneous microdamage (MDL thickness) in layered plates.

中文翻译：

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兰姆波传播二​​次谐波对固体板微损伤厚度的响应

摘要 本文从理论上和数值上研究了初级兰姆波传播的二次谐波产生对固体板微损伤层(MDL)厚度的响应特征。在这里，在非线性兰姆波传播分析中，具有 MDL 的实心板被视为双层板。在二阶微扰逼近和模态扩展分析的基础上，研究了主兰姆波在具有 MDL 的固体板中传播的累积倍频的物理过程。理论上分析了MDL厚度变化对满足低频区域近似相速度匹配的初级S 0 模式SHG效应的影响，然后进行了有限元 (FE) 模拟以验证理论预测的结果。理论分析和有限元模拟之间的密切一致性验证了使用主 S 0 模式的 SHG 效应来表征 MDL 厚度变化的有效性。此外，揭示了非线性声学参数随MDL厚度的变化机制，预计所得结果可为准确表征层状板中的非均匀微损伤（MDL厚度）提供方便的手段。