Expansion of Spherical Wave Functions for Electro-Magnetic Fields of a Vertical Magnetic Dipole over an Anisotropic Half-Space

2005 ◽  
Vol 48 (5) ◽  
pp. 1276-1282
Author(s):  
Bin-Hao JIANG ◽  
Yong-Tan LIU
Keyword(s):  
Magnetic Fields ◽  
Half Space ◽  
Magnetic Dipole ◽  
Spherical Wave ◽  
Wave Functions ◽  
Vertical Magnetic Dipole ◽  
Electro Magnetic

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 Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Doo-Sung Lee ◽  
Keyword(s):  
Half Space ◽  
Existence And Uniqueness ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Successive Approximations ◽  
Compressional Waves ◽  
Poroelastic Material ◽  
The Given

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

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