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Cumulative Second Harmonics in a Nonlinear Transversely Isotropic Plate

[+] Author Affiliations
Jinling Zhao, Jinhao Qiu

Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

Vamshi K. Chillara, Hwanjeong Cho, Cliff J. Lissenden

Penn State, University Park, PA

Paper No. SMASIS2015-9023, pp. V001T03A022; 6 pages
  • ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
  • Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems
  • Colorado Springs, Colorado, USA, September 21–23, 2015
  • Conference Sponsors: Aerospace Division
  • ISBN: 978-0-7918-5729-8
  • Copyright © 2015 by ASME


The problem of second harmonic guided wave generation in transversely isotropic plates is investigated from a theoretical and numerical standpoint. The strain energy function of transversely isotropic materials is written down using five invariants in terms of the Green-Lagrange strain tensor and contains five linear terms and nine nonlinear terms.

Theoretical investigations reveal that second harmonics in a weakly nonlinear transversely isotropic plate are cumulative only when the phase matching and nonzero power flux criteria are satisfied. Also, only cumulative secondary symmetric Lamb wave modes can be generated — a conclusion in line with what is observed for isotropic plates. Finally, numerical simulations are carried out to examine the cumulative second harmonic generation from the S0 mode and the results obtained are discussed in the light of the theory.

Copyright © 2015 by ASME



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