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Wave motion and dispersion phenomena: Veering, locking and strong coupling effects
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10.1121/1.3672647
/content/asa/journal/jasa/131/2/10.1121/1.3672647
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/2/10.1121/1.3672647

Figures

Image of FIG. 1.
FIG. 1.

Dispersion curves for simple waveguides, positive-going waves only: (a) – – – string under tension and ----- on elastic foundation; (b) – – – beam in bending and ----- on elastic foundation.

Image of FIG. 2.
FIG. 2.

Veering: dispersion curves for – – – uncoupled waveguides and ----- coupled waveguides, ɛ assumed real and positive, α 1>α 2 > 0. Inlays show directions of eigenvectors in (W 1 ,W 2) plane.

Image of FIG. 3.
FIG. 3.

Veering: (a) proportion of kinetic energy in waveguide 2 and (b) phase angle tan−1 W 2 /W 1 as functions of Ω: ----- upper branch and – – – lower branch of dispersion curves; ɛ assumed real and positive, q 1=q 2= 1, μ 1= 2μ 2, η= 2.

Image of FIG. 4.
FIG. 4.

Locking: (a) real and (b) imaginary dispersion curves for – – – uncoupled waveguides and ----- coupled waveguidesand (c), (d) wavenumber loci in the complex k-plane, ɛ assumed real and positive, α 1 ≥ 0, α 2 ≤ 0, α 1+α 2 > 0. Inlays show directions of eigenvectors in (W 1,W 2) plane.

Image of FIG. 5.
FIG. 5.

Locking: (a) proportion of kinetic energy in waveguide 2 and (b) phase angle tan–1 W 2 /W 1 as functions of Ω: ----- upper branch and – – – lower branch of dispersion curves; ɛ assumed real and positive, α 1= 1, α 2= –1, μ 1 = μ 2, v= 2.

Image of FIG. 6.
FIG. 6.

Stiffness-coupled system: (a) uncoupled disconnected system comprising beam in bending and a string under tension and lying on an elastic foundation S; (b) coupled system, with spring coupling s connecting the waveguides; (c) uncoupled blocked system.

Image of FIG. 7.
FIG. 7.

Dispersion curves: (a) uncoupled (disconnected) system; (b) uncoupled (blocked) system, showing strong coupling effects for the bending waves at low frequencies; (c) coupled system, showing veering, locking, unlocking and strong coupling effects; EI = T =  s =  b  = 1; S = 4; s = 0.36.

Image of FIG. 8.
FIG. 8.

Weak coupling effects in dispersion curves: (a) veering; (b) locking and unlocking, EI = T =  s  =  b  = 1; S = 4; s = 0.36; - - - -; wavenumbers in uncoupled blocked system and ----- wavenumbers in coupled system.

Image of FIG. 9.
FIG. 9.

Veering in damped string-beam system: (a) real and (b) imaginary parts of wavenumbers, EI = T = μs  =  b  = 1; S = 4; s = 0.36; ζb = 0; ----- ζs = 0, − · − · − ζs = 0.2, - - - ζs = 0.3, ζs  = 0.5.

Image of FIG. 10.
FIG. 10.

Two-dimensional acoustic duct with flexible side-wall.

Image of FIG. 11.
FIG. 11.

Dispersion curves for duct with flexible panel: - - - - uncoupled wavenumbers; ——propagating bending wave; − − −nearfield bending wave; − · − · −acoustic wave.

Tables

Generic image for table
TABLE I.

Dispersion phenomena in simple waveguides.

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/content/asa/journal/jasa/131/2/10.1121/1.3672647
2012-02-14
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Wave motion and dispersion phenomena: Veering, locking and strong coupling effects
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/2/10.1121/1.3672647
10.1121/1.3672647
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