An addition theorem for spherical wave functions

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

The Scattering Waves by Two Spheres in Solid

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.

Multiple scattering by a linear array of conducting spheres

1990 ◽  
Vol 68 (10) ◽  
pp. 1157-1165 ◽  
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.

Reconstruction of Acoustic Radiation of a Vibrating Structure Located in a Half-Space Bounded by a Passive Surface with Finite Acoustic Impedance

2020 ◽  
Vol 28 (04) ◽  
pp. 2050019
Author(s):  
Daren Zhou ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
Yongxiong Xiao
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Free Space ◽  
Plane Surface ◽  
Spherical Wave ◽  
Boundary Surface ◽  
Sound Field ◽  
Wave Functions ◽  
Reconstruction Method ◽  
Direct Radiation

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

scholarly journals Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
X. Garcia Santiago ◽  
M. Hammerschmidt ◽  
S. Burger ◽  
C. Rockstuhl ◽  
I. Fernandez-Corbaton ◽  
...  
Keyword(s):  
Electromagnetic Fields ◽  
Spherical Wave ◽  
Wave Functions

scholarly journals Sound Radiation due to Modal Vibrations of a Spherical Source in an Acoustic Quarterspace

2004 ◽  
Vol 11 (5-6) ◽  
pp. 625-635 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Mahdi Azarpeyvand
Keyword(s):  
Acoustic Radiation ◽  
Classical Method ◽  
Spherical Wave ◽  
Closed Form Solution ◽  
Addition Theorem ◽  
Form Solution ◽  
Surface Velocity ◽  
Rigid Boundary ◽  
Radiation Impedance ◽  
Spherical Source

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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