TY - JOUR
T1 - Mixing of collinear plane wave pulses in elastic solids with quadratic nonlinearity
AU - Chen, Zimu
AU - Tang, Guangxin
AU - Zhao, Youxun
AU - Jacobs, Laurence J.
AU - Qu, Jianmin
N1 - Publisher Copyright:
© 2014 Acoustical Society of America.
PY - 2014/11/1
Y1 - 2014/11/1
N2 - This paper derives a set of necessary and sufficient conditions for generating resonant waves by two propagating time-harmonic plane waves. It is shown that in collinear mixing, a resonant wave can be generated either by a pair of longitudinal waves, in which case the resonant mixing wave is also a longitudinal wave, or by a pair of longitudinal and transverse waves, in which case the resonant wave is a transverse wave. In addition, the paper obtains closed-form analytical solutions to the resonant waves generated by two collinearly propagating sinusoidal pulses. The results show that amplitude of the resonant pulse is proportional to the mixing zone size, which is determined by the spatial lengths of the input pulses. Finally, numerical simulations based on the finite element method and experimental measurements using one-way mixing are conducted. It is shown that both numerical and experimental results agree well with the analytical solutions.
AB - This paper derives a set of necessary and sufficient conditions for generating resonant waves by two propagating time-harmonic plane waves. It is shown that in collinear mixing, a resonant wave can be generated either by a pair of longitudinal waves, in which case the resonant mixing wave is also a longitudinal wave, or by a pair of longitudinal and transverse waves, in which case the resonant wave is a transverse wave. In addition, the paper obtains closed-form analytical solutions to the resonant waves generated by two collinearly propagating sinusoidal pulses. The results show that amplitude of the resonant pulse is proportional to the mixing zone size, which is determined by the spatial lengths of the input pulses. Finally, numerical simulations based on the finite element method and experimental measurements using one-way mixing are conducted. It is shown that both numerical and experimental results agree well with the analytical solutions.
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U2 - 10.1121/1.4896567
DO - 10.1121/1.4896567
M3 - Article
AN - SCOPUS:84908575905
SN - 0001-4966
VL - 136
SP - 2389
EP - 2404
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
IS - 5
ER -