Electromagnetic Multiple PEC Object Scattering Using Equivalence Principle and Addition Theorem for Spherical Wave Harmonics

Radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace is analyzed in an exact manner. The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the pulsating (n= 0) and translational oscillating (n= 1) modes, is positioned near the rigid boundary of a water-filled quarterspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.

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The Scattering Waves by Two Spheres in Solid

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.423-426.1640 ◽

2013 ◽

Vol 423-426 ◽

pp. 1640-1643

Author(s):

Yan Ru Zhang ◽

Pei Jun Wei

Keyword(s):

Wave Function ◽

Cross Section ◽

Spherical Wave ◽

Addition Theorem ◽

Wave Functions ◽

Interface Condition ◽

Elastic Sphere ◽

Numerical Examples ◽

Transmitted Waves ◽

Expansion Coefficients

The scattering waves by two elastic spheres in solid are studied. The incident wave, the scattering waves in the host and the transmitted waves in the elastic spheres are all expanded in the series form of spherical wave functions. The total waves are obtained by addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the solid host. The scattering cross section is computed as numerical examples.

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An addition theorem for spherical wave functions

Lettere al Nuovo Cimento ◽

10.1007/bf02754705 ◽

1982 ◽

Vol 35 (11) ◽

pp. 353-357

Author(s):

L. Ronchi ◽

S. Barbarino ◽

P. Grasso ◽

G. Guerriera ◽

F. Musumeci ◽

...

Keyword(s):

Spherical Wave ◽

Addition Theorem ◽

Wave Functions

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Multiple scattering by a linear array of conducting spheres

Canadian Journal of Physics ◽

10.1139/p90-163 ◽

1990 ◽

Vol 68 (10) ◽

pp. 1157-1165 ◽

Cited By ~ 16

Author(s):

A-K. Hamid ◽

I. R. Ciric ◽

M. Hamid

Keyword(s):

Multiple Scattering ◽

Cross Sections ◽

Linear Array ◽

Plane Electromagnetic Wave ◽

Spherical Wave ◽

Approximate Solutions ◽

Addition Theorem ◽

Wave Functions ◽

Coordinate Systems ◽

Conducting Spheres

The problem of multiple scattering of a plane electromagnetic wave incident on N closely spaced perfectly conducting spheres is solved analytically by expanding the incident and scattering fields in terms of an appropriate set of vector spherical wave functions. To impose the boundary conditions, the scattered field from one sphere is expressed in coordinate systems attached to the others by using the translation addition theorem. An approximate solution is obtained to solve for the scattering by N small spheres. Numerical results for the normalized backscattering and bistatic cross sections for systems of spheres show that the agreement between the analytic and approximate solutions is better for larger electrical distances between neighbouring spheres.

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The Scattering of Acoustic Wave by a Chain of Elastic Spheres in Liquid

Journal of Vibration and Acoustics ◽

10.1115/1.4026434 ◽

2014 ◽

Vol 136 (2) ◽

Cited By ~ 1

Author(s):

Yanru Zhang ◽

Peijun Wei

Keyword(s):

Acoustic Waves ◽

Scattering Amplitude ◽

Spherical Wave ◽

Addition Theorem ◽

Interface Condition ◽

Numerical Examples ◽

Transmitted Waves ◽

Scattering Wave ◽

Expansion Coefficients ◽

A Chain

The scattering of acoustic waves by a chain of elastic spheres in liquid is studied. The incident wave, the scattering wave in the host, and the transmitted waves (including longitudinal and transverse wave modes) in the elastic spheres are all expanded in the form of a series of spherical wave functions. The total waves are obtained by the addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the liquid host. The scattering cross section and the scattering amplitude in far field are computed as numerical examples. Two cases, steel spheres and lead spheres embedded in water, are considered in the numerical examples.

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