Analytical study of dispersion relations for shear horizontal wave propagation in plates with periodic stubs

Handle URI:
http://hdl.handle.net/10754/564197
Title:
Analytical study of dispersion relations for shear horizontal wave propagation in plates with periodic stubs
Authors:
Xu, Yanlong
Abstract:
The coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures' evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates. © 2015 Elsevier B.V.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Ultrasonics
Issue Date:
Aug-2015
DOI:
10.1016/j.ultras.2015.04.004
Type:
Article
ISSN:
0041624X
Sponsors:
This work is supported by the KAUST Baseline Research Fund.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Yanlongen
dc.date.accessioned2015-08-03T12:36:04Zen
dc.date.available2015-08-03T12:36:04Zen
dc.date.issued2015-08en
dc.identifier.issn0041624Xen
dc.identifier.doi10.1016/j.ultras.2015.04.004en
dc.identifier.urihttp://hdl.handle.net/10754/564197en
dc.description.abstractThe coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures' evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates. © 2015 Elsevier B.V.en
dc.description.sponsorshipThis work is supported by the KAUST Baseline Research Fund.en
dc.publisherElsevier BVen
dc.subjectBand structuresen
dc.subjectDispersion relationsen
dc.subjectShear horizontal guided waveen
dc.titleAnalytical study of dispersion relations for shear horizontal wave propagation in plates with periodic stubsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalUltrasonicsen
kaust.authorXu, Yanlongen
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