The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components.

中文翻译：

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闭合平行裂纹处二次谐波的最低阶反对称兰姆波生成

通过数值分析，研究了弹性板闭合平行裂纹中基本反对称兰姆波的二次谐波产生。闭合裂纹被建模为具有二次非线性的弹簧型界面。基于摄动方法，非线性兰姆波散射问题被分解为两个线性化问题，即，裂纹处入射兰姆波的线性反射/透射以及由于裂纹引起的二次谐波兰姆波的产生/辐射接触非线性。减少的问题通过频域中的有限元方法解决。数值结果表明，裂纹共振对线性和非线性兰姆波散射响应具有显着影响，在反射/透射光谱中表现为尖锐的峰/谷，在某些频率下增强的二次谐波振幅。建立了两个简单的频率选择规则，它们解释了二次谐波兰姆波的增强生成。还进行了时域分析以补充频域分析，该分析确认了入射兰姆波有选择地与裂纹在其带宽中的某些特定频率处相互作用，并增强了第二谐波分量的生成。