Frequency Dependence of Second-Harmonic Generation in Lamb Waves
Frequency Dependence of Second-Harmonic Generation in Lamb Waves
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DOI：
10.1007/s10921-014-0227-y
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发表时间：
2014-06-01
影响因子：
2.8
通讯作者：
Biwa, Shiro
中科院分区：
文献类型：
--
作者：
Matsuda, Naoki;Biwa, Shiro
为了研究相位匹配对材料非线性敏感评价的作用，从理论和数值上研究了兰姆波中二次谐波产生的频率依赖性。利用微扰技术和满足相位匹配的典型频率附近的模态分解，分析了各向同性板中非线性兰姆波的传播。结果表明，在一定的基频范围内，在有限的传输距离内，二次谐波兰姆模的振幅与基波兰姆模振幅的平方之比是累积增长的。当传输距离有限时，该比值达到最大值的频率接近但不等于相位匹配频率。这一特点是确认使用有限差分时域方法，将材料和几何非线性数值。二次谐波模式的振幅在基频的有限范围内变高的事实证明了使用兰姆波中的二次谐波的材料评估方法的鲁棒性。
The frequency dependence of the second-harmonic generation in Lamb waves is studied theoretically and numerically in order to examine the role of phase matching for sensitive evaluation of material nonlinearity. Nonlinear Lamb wave propagation in an isotropic plate is analyzed using the perturbation technique and the modal decomposition in the neighborhood of a typical frequency satisfying the phase matching. The results show that the ratio of the amplitude of second-harmonic Lamb mode to the squared amplitude of fundamental Lamb mode grows cumulatively in a certain range of fundamental frequency for a finite propagation distance. It is also shown that the frequency for which this ratio reaches maximum is close but not equal to the phase-matching frequency when the propagation distance is finite. This feature is confirmed numerically using the finite-difference time-domain method incorporating material and geometrical nonlinearities. The fact that the amplitude of second-harmonic mode becomes high in a finite range of fundamental frequency proves robustness of the material evaluation method using second harmonics in Lamb waves.