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Frequency Dependence of Second-Harmonic Generation in Lamb Waves

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Abstract

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.

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Acknowledgments

This work has been supported by JSPS KAKENHI Grant Numbers 24\(\cdot \)2517 and 25289005.

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  1. Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 615-8540, Japan

    Naoki Matsuda & Shiro Biwa

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  1. Naoki Matsuda
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  2. Shiro Biwa
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Correspondence to Shiro Biwa.

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Matsuda, N., Biwa, S. Frequency Dependence of Second-Harmonic Generation in Lamb Waves. J Nondestruct Eval 33, 169–177 (2014). https://doi.org/10.1007/s10921-014-0227-y

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