Interaction of torsional and longitudinal guided waves in weakly nonlinear circular cylinders

Yang Liu, Ehsan Khajeh, Clifford Jesse Lissenden, III, Joseph Lawrence Rose

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on an isotropic homogeneous weakly nonlinear elastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental waves in a circular cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wave structures are manipulated to analyze the higher harmonic generation due to the guided wave mode self-interactions and mutual interactions. It is proved that both torsional and longitudinal secondary wave fields can be cumulative by a specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strong cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Nonlinear finite element simulations demonstrate second harmonic generation by T(0,3) and L(0,4) modes at the internal resonance points. A linear increase of the normalized modal amplitude ratio A 2 / A 1 2 over the propagation distance is observed for both cases, which indicates that mode L(0,5) is effectively generated as a cumulative second harmonic. Counter numerical examples demonstrate that synchronism and sufficient power flux from the fundamental mode to the secondary mode must occur for the secondary wave field to be strongly cumulative.

Original languageEnglish (US)
Pages (from-to)2541-2553
Number of pages13
JournalJournal of the Acoustical Society of America
Volume133
Issue number5
DOIs
StatePublished - May 1 2013

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circular cylinders
interactions
harmonic generations
S waves
harmonics
spherical coordinates
longitudinal waves
Cylinder
Interaction
Waves
wave equations
synchronism
counters
Harmonics
propagation
matrices
excitation
Fundamental
simulation

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

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abstract = "The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on an isotropic homogeneous weakly nonlinear elastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental waves in a circular cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wave structures are manipulated to analyze the higher harmonic generation due to the guided wave mode self-interactions and mutual interactions. It is proved that both torsional and longitudinal secondary wave fields can be cumulative by a specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strong cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Nonlinear finite element simulations demonstrate second harmonic generation by T(0,3) and L(0,4) modes at the internal resonance points. A linear increase of the normalized modal amplitude ratio A 2 / A 1 2 over the propagation distance is observed for both cases, which indicates that mode L(0,5) is effectively generated as a cumulative second harmonic. Counter numerical examples demonstrate that synchronism and sufficient power flux from the fundamental mode to the secondary mode must occur for the secondary wave field to be strongly cumulative.",
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Interaction of torsional and longitudinal guided waves in weakly nonlinear circular cylinders. / Liu, Yang; Khajeh, Ehsan; Lissenden, III, Clifford Jesse; Rose, Joseph Lawrence.

In: Journal of the Acoustical Society of America, Vol. 133, No. 5, 01.05.2013, p. 2541-2553.

Research output: Contribution to journalArticle

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