Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

doi:10.1088/1674-1056/19/11/114302

Abstract Within the second-order perturbation approximation, this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate. The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero. It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave, the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic. It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied. Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance. Furthermore, it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation. The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.

Keywords: Lamb wave second-harmonic generation group velocity matching phase velocity matching

Received: 31 March 2010
Revised: 25 April 2010
Accepted manuscript online:

PACS:	43.25.Cb	(Macrosonic propagation, finite amplitude sound; shock waves)
	43.25.Ed	(Effect of nonlinearity on velocity and attenuation)

Fund: Project supported by the National Natural Science Foundation of China (Grant No 10974256).

Cite this article:

Deng Ming-Xi(邓明晰) and Xiang Yan-Xun(项延训) Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate 2010 Chin. Phys. B 19 114302

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Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

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