Journal of Nondestructive Evaluation

, Volume 33, Issue 2, pp 169–177 | Cite as

Frequency Dependence of Second-Harmonic Generation in Lamb Waves

  • Naoki Matsuda
  • Shiro Biwa


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.


Nonlinear ultrasonics Higher harmonic generation Lamb wave Perturbation analysis  Finite-difference time-domain method 



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


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Aeronautics and Astronautics, Graduate School of EngineeringKyoto UniversityKyotoJapan

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