TY - JOUR
T1 - Second harmonic generation in composites
T2 - Theoretical and numerical analyses
AU - Zhao, Jinling
AU - Chillara, Vamshi K.
AU - Ren, Baiyang
AU - Cho, Hwanjeong
AU - Qiu, Jinhao
AU - Lissenden, Cliff J.
N1 - Publisher Copyright:
© 2016 AIP Publishing LLC.
PY - 2016/2/14
Y1 - 2016/2/14
N2 - Second harmonic generation in a transversely isotropic plate and a symmetric composite laminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric composite laminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric composite laminates.
AB - Second harmonic generation in a transversely isotropic plate and a symmetric composite laminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric composite laminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric composite laminates.
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U2 - 10.1063/1.4941390
DO - 10.1063/1.4941390
M3 - Article
AN - SCOPUS:84958580919
SN - 0021-8979
VL - 119
JO - Journal of Applied Physics
JF - Journal of Applied Physics
IS - 6
M1 - 064902
ER -