Harmonic Generation at a Nonlinear Imperfect Joint of Plates by the S0 Lamb Wave Incidence

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear springtype interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity.

通过微扰分析和时域数值模拟，研究了最低阶对称（S0）兰姆波入射时兰姆波与板的非理想连接的非线性相互作用。非理想连接被建模为非线性弹簧型界面，该界面将界面应力表示为位移不连续的函数。在微扰分析中，在弱非线性假设下，利用薄板近似和拉伸波在频域中研究了连接处的二次谐波产生。结果表明，在低频范围内，二次谐波拉伸波的振幅与S0模式的结果吻合良好。然而，发现薄板近似无法重现由于连接共振而出现的二次谐波S0模式的放大。此外，通过弹性动力学有限积分技术（EFIT）进行了时域分析。当入射波振幅相对较大时，基波和二次谐波表现出与微扰分析结果不同的行为。具体而言，如果入射振幅增加，二次谐波振幅的峰值频率会降低。还基于弱非线性的结果对非线性相互作用的瞬态行为进行了研究和讨论。