Ye Tianming, Biwa Shiro, Mori Naoki
Institute of Acoustics, Tongji University, No. 1239 Siping Road, Shanghai 200092, China.
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8540, Japan.
J Acoust Soc Am. 2020 Oct;148(4):2073. doi: 10.1121/10.0002171.
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.
通过数值分析研究了弹性板中闭合平行裂纹处基本反对称兰姆波的二次谐波产生。将闭合裂纹建模为具有二次非线性的弹簧型界面。基于微扰方法，将非线性兰姆波散射问题分解为两个线性化问题，即入射兰姆波在裂纹处的线性反射/透射问题以及由于接触非线性导致的二次谐波兰姆波的产生/辐射问题。通过频域有限元方法求解简化后的问题。数值结果表明裂纹共振对线性和非线性兰姆波散射响应有显著影响，表现为反射/透射谱中的尖锐峰值/凹陷以及某些频率下增强的二次谐波振幅。建立了两条简单的频率选择规则，解释了二次谐波兰姆波的增强产生。还进行了时域分析以补充频域分析，证实入射兰姆波在其带宽内的某些特定频率下以选择性方式与裂纹相互作用，并增强了二次谐波分量的产生。
