复合固体层中兰姆波的积累二次谐波发生与传播研究

文章提出一种分析复合固体层中兰姆波的积累二次谐波发生与传播的方法。基于导波的部分平面波分析理论，建立了复合固体层中非线性兰姆的理论模型。在分析过程中，将非线性作为线性情形的二阶微扰进行处理的方法。尽管复合固体层中兰姆波具有频散性质，分析结果表明，对于一些特定条件，二次谐波的振幅可以随传播距离积累增长。根据边界条件和初始激发条件，得到积累二次谐波的形式解，在此基础上进行了数值分析，给出一些有趣的声场分布。

Analysis of generation of cumulative second harmonic of Lamb mode in a composited layer

In this article we have developed a technique for analyzing the nonlinear generation of cumulative second harmonic of a Lamb mode in a composited layer. A theoretical model for nonlinear Lamb mode propagation in a composited layer has been established, based on a partial plane wave approach. The nonlinearity is treated as the second-order perturbation of the linear elastic response. Although Lamb mode propagation is dispersive in a composited layer, the analysis results show that the amplitudes of the second harmonic of Lamb mode do accumulate with propagation distance under certain special conditions. Based on the boundary and initial conditions of excitation, the formal solution to the cumulative second harmonic is derived. Using the formal solution, we have performed some numerical simulations and obtained some interesting distribution of acoustic field patterns.