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Dictums for problem solving and approximation in mathematical acoustics: Examples involving low-frequency vibration and radiation
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10.1121/1.3680605
/content/asa/journal/jasa/131/3/10.1121/1.3680605
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/3/10.1121/1.3680605
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch illustrating the problem of acoustic radiation caused by the vibrations of a long rigid cylinder oscillating in a compliant baffle.

Image of FIG. 2.
FIG. 2.

Sketch illustrating terminology used in the statement of the acoustic energy corollary in terms of volume and surface integrals.

Image of FIG. 3.
FIG. 3.

Sketch illustrating the use of the energy corollary for transient radiation from the moving cylinder. The outer radius is selected to be so large that the disturbance has not yet reached that radius.

Image of FIG. 4.
FIG. 4.

Sketch illustrating the problem of the radiation of surface waves and other pressure disturbances by an oscillating horizontal cylinder on the surface of a fluid bounded by a compliant surface.

Image of FIG. 5.
FIG. 5.

General sketch of the complex plane for the complex angular velocity ω, indicating general location of singularities for the Fourier transform of a function of time that is zero before some initial time.

Image of FIG. 6.
FIG. 6.

Sketch illustrating the concepts of inner and outer regions for problems involving an oscillating cylinder at the edge of a half-space.

Image of FIG. 7.
FIG. 7.

Sketch illustrating the concept of an outgoing cylindrical wave as being a superposition of waves from point sources spaced along the symmetry axis.

Image of FIG. 8.
FIG. 8.

Deformed contour used as an initial step for the determination of an approximate expression of the outer solution for small arguments.

Image of FIG. 9.
FIG. 9.

Sketch showing location of hypothetical line source and image source used in the mathematical construction of an outer solution for the general problem discussed in the present paper. The vibrating interface serves as a third source in the construction.

Image of FIG. 10.
FIG. 10.

Selection of branch cuts and location of poles for the contour integration when the Hankel function is represented as a Fourier transform involving an integration over the horizontal wave number.

Image of FIG. 11.
FIG. 11.

Resulting path of integration in the complex horizontal wavenumber plane in the limit when the artificial damping parameter goes to zero. (The poles appear when the possibility of surface waves is taken into account.)

Image of FIG. 12.
FIG. 12.

Deformed contour for the outer solution of the general problem discussed in the present paper, the deformation being such that a term corresponding to an outwardly propagating surface wave is evident.

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/content/asa/journal/jasa/131/3/10.1121/1.3680605
2012-03-15
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dictums for problem solving and approximation in mathematical acoustics: Examples involving low-frequency vibration and radiation
http://aip.metastore.ingenta.com/content/asa/journal/jasa/131/3/10.1121/1.3680605
10.1121/1.3680605
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