Cumulative second harmonics in a nonlinear transversely isotropic plate

Jinling Zhao; Vamshi K. Chillara; Hwanjeong Cho; Jinhao Qiu; Cliff J. Lissenden

doi:10.1115/SMASIS2015-9023

Cumulative second harmonics in a nonlinear transversely isotropic plate

Jinling Zhao, Vamshi K. Chillara, Hwanjeong Cho, Jinhao Qiu, Cliff J. Lissenden

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	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
ISBN (Electronic)	9780791857298
DOIs	https://doi.org/10.1115/SMASIS2015-9023
State	Published - 2015
Event	ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 - Colorado Springs, United States Duration: Sep 21 2015 → Sep 23 2015

Publication series

Name	ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015
Volume	1

Other

Other	ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015
Country/Territory	United States
City	Colorado Springs
Period	9/21/15 → 9/23/15

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1115/SMASIS2015-9023

Cite this

Zhao, J., Chillara, V. K., Cho, H., Qiu, J., & Lissenden, 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 (ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015; Vol. 1). American Society of Mechanical Engineers. https://doi.org/10.1115/SMASIS2015-9023

Zhao, Jinling ; Chillara, Vamshi K. ; Cho, Hwanjeong et al. / 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. American Society of Mechanical Engineers, 2015. (ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015).

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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, {Cliff J.}",

note = "Publisher Copyright: {\textcopyright} Copyright 2015 by ASME.; ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 ; Conference date: 21-09-2015 Through 23-09-2015",

year = "2015",

doi = "10.1115/SMASIS2015-9023",

language = "English (US)",

series = "ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015",

publisher = "American Society of Mechanical Engineers",

booktitle = "Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems",

}

Zhao, J, Chillara, VK, Cho, H, Qiu, J & Lissenden, 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. ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015, 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 et al.
Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems. American Society of Mechanical Engineers, 2015. (ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference 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, Cliff J.

PY - 2015

Y1 - 2015

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.

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M3 - Conference contribution

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

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Zhao J, Chillara VK, Cho H, Qiu J, Lissenden 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. American Society of Mechanical Engineers. 2015. (ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015). doi: 10.1115/SMASIS2015-9023

Cumulative second harmonics in a nonlinear transversely isotropic plate

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