TY - JOUR
T1 - Second Harmonic Generation of Shear Waves in Crystals
AU - Jiang, Wenhua
AU - Cao, Wenwu
N1 - Funding Information:
Manuscript received May 22, 2003; accepted September 15, 2003. This research is supported by NIH under Grant #P41RR11795. The authors are with The Pennsylvania State University, University Park, Pennsylvania 16802 (e-mail: [email protected]).
PY - 2004/2
Y1 - 2004/2
N2 - Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6mm and 3m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO 3) crystal, and its third-order elastic constant c 444 is determined.
AB - Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6mm and 3m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO 3) crystal, and its third-order elastic constant c 444 is determined.
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U2 - 10.1109/TUFFC.2004.1295390
DO - 10.1109/TUFFC.2004.1295390
M3 - Article
C2 - 15055805
AN - SCOPUS:1642618223
SN - 0885-3010
VL - 51
SP - 153
EP - 162
JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
IS - 2
ER -