Cumulative second harmonics in a nonlinear transversely isotropic plate

Jinling Zhao, Vamshi K. Chillara, Hwanjeong Cho, Jinhao Qiu, Clifford Jesse Lissenden, III

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationDevelopment and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems
PublisherAmerican Society of Mechanical Engineers
Volume1
ISBN (Electronic)9780791857298
DOIs
StatePublished - Jan 1 2015
EventASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 - Colorado Springs, United States
Duration: Sep 21 2015Sep 23 2015

Other

OtherASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015
CountryUnited States
CityColorado Springs
Period9/21/159/23/15

Fingerprint

Phase matching
Guided electromagnetic wave propagation
Harmonic generation
Strain energy
Surface waves
Tensors
Fluxes
Computer simulation

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Mechanics of Materials
  • Building and Construction

Cite this

Zhao, J., Chillara, V. K., Cho, H., Qiu, J., & Lissenden, III, C. J. (2015). Cumulative second harmonics in a nonlinear transversely isotropic plate. In Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems (Vol. 1). American Society of Mechanical Engineers. https://doi.org/10.1115/SMASIS2015-9023
Zhao, Jinling ; Chillara, Vamshi K. ; Cho, Hwanjeong ; Qiu, Jinhao ; Lissenden, III, Clifford Jesse. / Cumulative second harmonics in a nonlinear transversely isotropic plate. Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems. Vol. 1 American Society of Mechanical Engineers, 2015.
@inproceedings{fa0217f75be64c92b5c6f018c578e983,
title = "Cumulative second harmonics in a nonlinear transversely isotropic plate",
abstract = "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.",
author = "Jinling Zhao and Chillara, {Vamshi K.} and Hwanjeong Cho and Jinhao Qiu and {Lissenden, III}, {Clifford Jesse}",
year = "2015",
month = "1",
day = "1",
doi = "10.1115/SMASIS2015-9023",
language = "English (US)",
volume = "1",
booktitle = "Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems",
publisher = "American Society of Mechanical Engineers",

}

Zhao, J, Chillara, VK, Cho, H, Qiu, J & Lissenden, III, CJ 2015, Cumulative second harmonics in a nonlinear transversely isotropic plate. in Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems. vol. 1, American Society of Mechanical Engineers, ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015, Colorado Springs, United States, 9/21/15. https://doi.org/10.1115/SMASIS2015-9023

Cumulative second harmonics in a nonlinear transversely isotropic plate. / Zhao, Jinling; Chillara, Vamshi K.; Cho, Hwanjeong; Qiu, Jinhao; Lissenden, III, Clifford Jesse.

Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems. Vol. 1 American Society of Mechanical Engineers, 2015.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Cumulative second harmonics in a nonlinear transversely isotropic plate

AU - Zhao, Jinling

AU - Chillara, Vamshi K.

AU - Cho, Hwanjeong

AU - Qiu, Jinhao

AU - Lissenden, III, Clifford Jesse

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966600752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966600752&partnerID=8YFLogxK

U2 - 10.1115/SMASIS2015-9023

DO - 10.1115/SMASIS2015-9023

M3 - Conference contribution

AN - SCOPUS:84966600752

VL - 1

BT - Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems

PB - American Society of Mechanical Engineers

ER -

Zhao J, Chillara VK, Cho H, Qiu J, Lissenden, III CJ. Cumulative second harmonics in a nonlinear transversely isotropic plate. In Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems. Vol. 1. American Society of Mechanical Engineers. 2015 https://doi.org/10.1115/SMASIS2015-9023