Sound radiation from stationary and rotating point acoustic sources with shield of rigid prolate spheroidal baffles is explored in the prolate spheroidal coordinate system. The formulae of far-field sound pressure and acoustic power are derived and acoustic power spectral density (PSD) in terms of circumferential and azimuthal wavenumber is manifested from the low frequency range to high frequency range. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Rotating sound sources cause the frequency veering phenomenon and change the patterns of PSD. Some spheroidal harmonic waves with lower and higher wavenumber for the large prolate spheroids cannot contribute to far-field sound radiation in the high frequency range when sound sources are close to the axes of the spheroids. Sound pressure directivity and acoustic power of stationary point sound sources are also analyzed with the variation of source location.

References

References
1.
Padula
,
S. L.
, and
Liu
,
C. H.
,
1978
, “
Acoustic Scattering of Point Sources by a Moving Prolate Spheroid
,”
AIAA J.
,
16
(
6
), pp.
551
552
.
2.
Rhee
,
S. H.
, and
Hino
,
T.
,
2002
, “
Numerical Simulation of Unsteady Turbulent Flow Around Maneuvering Prolate Spheroid
,”
AIAA J.
,
40
(
10
), pp.
2017
2026
.
3.
Boisvert
,
J. E.
, and
Van Buren
,
A. L.
,
2004
, “
Acoustic Directivity of Rectangular Pistons on Prolate Spheroids
,”
J. Acoust. Soc. Am.
,
116
(
4
), pp.
1932
1937
.
4.
Chertock
,
G.
,
1961
, “
Sound Radiation From Prolate Spheroids
,”
J. Acoust. Soc. Am.
,
33
(
7
), pp.
871
876
.
5.
Buren
,
A. L. V.
,
1971
, “
Acoustic Radiation Impedance of Caps and Rings on Prolate Spheroids
,”
J. Acoust. Soc. Am.
,
50
(
5B
), pp.
1343
1356
.
6.
Baier
,
R. V.
,
1972
, “
Acoustic Radiation Impedance of Caps and Rings on Oblate Spheroidal Baffles
,”
J. Acoust. Soc. Am.
,
51
(
5B
), pp.
1705
1716
.
7.
Boisvert
,
J. E.
, and
Van Buren
,
A. L.
,
2002
, “
Acoustic Radiation Impedance of Rectangular Pistons on Prolate Spheroids
,”
J. Acoust. Soc. Am.
,
111
(
2
), pp.
867
874
.
8.
Buren
,
A. L. V.
, and
King
,
B. J.
,
1972
, “
Acoustic Radiation From Two Spheroids
,”
J. Acoust. Soc. Am.
,
52
(
1B
), pp.
364
372
.
9.
Mitri
,
F. G.
,
2015
, “
Acoustic Radiation Force on Oblate and Prolate Spheroids in Bessel Beams
,”
Wave Motion
,
57
, pp.
231
238
.
10.
Spence
,
R. D.
,
1948
, “
The Diffraction of Sound by Circular Disks and Apertures
,”
J. Acoust. Soc. Am.
,
20
(
4
), pp.
380
386
.
11.
Spence
,
R. D.
, and
Granger
,
S.
,
1951
, “
The Scattering of Sound From a Prolate Spheroid
,”
J. Acoust. Soc. Am.
,
23
(
6
), pp.
701
706
.
12.
Einspruch
,
N. G.
, and
Barlow
, and
C. A.
, Jr.
,
1961
, “
Scattering of a Compressional Wave by a Prolate Spheroid
,”
Q. Appl. Math.
,
19
(
3
), pp.
253
258
.
13.
Silbiger
,
A.
,
1963
, “
Scattering of Sound by an Elastic Prolate Spheroid
,”
J. Acoust. Soc. Am.
,
35
(
4
), pp.
564
570
.
14.
Burke
,
J. E.
,
1966
, “
Long-Wavelength Scattering by Hard Spheroids
,”
J. Acoust. Soc. Am.
,
40
(
2
), pp.
325
330
.
15.
Burke
,
J. E.
,
1966
, “
Low-Frequency Scattering by Soft Spheroids
,”
J. Acoust. Soc. Am.
,
39
(
5A
), pp.
826
831
.
16.
Yeh
,
C.
,
1967
, “
Scattering of Acoustic Waves by a Penetrable Prolate Spheroid—I: Liquid Prolate Spheroid
,”
J. Acoust. Soc. Am.
,
42
(
2
), pp.
518
521
.
17.
Burke
,
J. E.
,
1968
, “
Scattering by Penetrable Spheroids
,”
J. Acoust. Soc. Am.
,
43
(
4
), pp.
871
875
.
18.
Van Bladel
,
J.
,
1968
, “
Low-Frequency Scattering by Hard and Soft Bodies
,”
J. Acoust. Soc. Am.
,
44
(
4
), pp.
1069
1073
.
19.
Lauchle
,
G. C.
,
1975
, “
Short-Wavelength Acoustic Backscattering by a Prolate Spheroid
,”
J. Acoust. Soc. Am.
,
58
(
3
), pp.
576
580
.
20.
Sammelmann
,
G. S.
,
Trivett
,
D. H.
, and
Hackman
,
R. H.
,
1988
, “
High-Frequency Scattering From Rigid Prolate Spheroids
,”
J. Acoust. Soc. Am.
,
83
(
1
), pp.
46
54
.
21.
Varadan
,
V. K.
,
Varadan
,
V. V.
,
Su
,
J. H.
, and
Pillai
,
T. A. K.
,
1982
, “
Comparison of Sound Scattering by Rigid and Elastic Obstacles in Water
,”
J. Acoust. Soc. Am.
,
71
(
6
), pp.
1377
1383
.
22.
Hackman
,
R. H.
,
Sammelmann
,
G. S.
,
Williams
,
K. L.
, and
Trivett
,
D. H.
,
1988
, “
A Reanalysis of the Acoustic Scattering From Elastic Spheroids
,”
J. Acoust. Soc. Am.
,
83
(
4
), pp.
1255
1266
.
23.
Stanton
,
T. K.
,
1990
, “
Sound Scattering by Spherical and Elongated Shelled Bodies
,”
J. Acoust. Soc. Am.
,
88
(
3
), pp.
1619
1633
.
24.
Ye
,
Z.
,
Hoskinson
,
E.
,
Dewey
,
R. K.
,
Ding
,
L.
, and
Farmer
,
D. M.
,
1997
, “
A Method for Acoustic Scattering by Slender Bodies—I: Theory and Verification
,”
J. Acoust. Soc. Am.
,
102
(
4
), pp.
1964
1976
.
25.
Adelman
,
R.
,
Gumerov
,
N. A.
, and
Duraiswami
,
R.
,
2014
, “
Semi-Analytical Computation of Acoustic Scattering by Spheroids and Disks
,”
J. Acoust. Soc. Am.
,
136
(
6
), pp.
EL405
EL410
.
26.
Gonzalez
,
J. D.
,
Lavia
,
E. F.
, and
Blanc
,
S.
,
2016
, “
A Computational Method to Calculate the Exact Solution for Acoustic Scattering by Fluid Spheroids
,”
Acta Acust. Acust.
,
102
(
6
), pp.
1061
1071
.
27.
Roumeliotis
,
J. A.
,
Kotsis
,
A. D.
, and
Kolezas
,
G.
,
2007
, “
Acoustic Scattering by an Impenetrable Spheroid
,”
Acoust. Phys.
,
53
(
4
), pp.
436
447
.
28.
Kotsis
,
A. D.
, and
Roumeliotis
,
J. A.
,
2008
, “
Acoustic Scattering by a Penetrable Spheroid
,”
Acoust. Phys.
,
54
(
2
), pp.
153
167
.
29.
Abbasov
,
I. B.
,
2008
, “
Study of the Scattering of Nonlinearly Interacting Plane Acoustic Waves by an Elongated Spheroid
,”
J. Sound Vib.
,
309
(
1–2
), pp.
52
62
.
30.
Andronov
,
I. V.
,
2011
, “
Diffraction by a Strongly Elongated Body of Revolution
,”
Acoust. Phys.
,
57
(
2
), pp.
121
126
.
31.
Andronov
,
I. V.
,
2012
, “
Diffraction of a Plane Wave Incident at a Small Angle to the Axis of a Strongly Elongated Spheroid
,”
Acoust. Phys.
,
58
(
5
), pp.
521
529
.
32.
Andronov
,
I. V.
,
2013
, “
High-Frequency Acoustic Scattering From Prolate Spheroids With High Aspect Ratio
,”
J. Acoust. Soc. Am.
,
134
(
6
), pp.
4307
4315
.
33.
Popov
,
M. M.
, and
Kirpichnikova
,
N. Y.
,
2014
, “
On Problems of Applying the Parabolic Equation to Diffraction by Prolate Bodies
,”
Acoust. Phys.
,
60
(
4
), pp.
363
370
.
34.
Kleev
,
A. I.
, and
Kyurkchan
,
A. G.
,
2015
, “
Application of the Pattern Equation Method in Spheroidal Coordinates to Solving Diffraction Problems With Highly Prolate Scatterers
,”
Acoust. Phys.
,
61
(
1
), pp.
19
27
.
35.
Miloh
,
T.
,
2016
, “
Acoustic Scattering on Spheroidal Shapes Near Boundaries
,”
Acoust. Phys.
,
62
(
6
), pp.
663
671
.
36.
Charalambopoulos
,
A.
,
Dassios
,
G.
,
Fotiadis
,
D. I.
, and
Massalas
,
C. V.
,
2001
, “
Scattering of a Point Generated Field by a Multilayered Spheroid
,”
Acta Mech.
,
150
(
1–2
), pp.
107
119
.
37.
Charalambopoulos
,
A.
,
Fotiadis
,
D. I.
, and
Massalas
,
C. V.
,
2002
, “
Scattering of a Point Generated Field by Kidney Stones
,”
Acta Mech.
,
153
(
1–2
), pp.
63
77
.
38.
Anagnostopoulos
,
K. A.
,
Mavratzas
,
S.
,
Charalambopoulos
,
A.
, and
Fotiadis
,
D. I.
,
2003
, “
Scattering of a Spherical Acoustic Field From an Eccentric Spheroidal Structure Simulating the Kidney-Stone System
,”
Acta Mech.
,
161
(
1–2
), pp.
39
52
.
39.
Rapids
,
B. R.
, and
Lauchle
,
G. C.
,
2006
, “
Vector Intensity Field Scattered by a Rigid Prolate Spheroid
,”
J. Acoust. Soc. Am.
,
120
(
1
), pp.
38
48
.
40.
Kokkorakis
,
G. C.
, and
Roumeliotis
,
J. A.
,
1997
, “
Acoustic Eigenfrequencies in Concentric Spheroidal–Spherical Cavities
,”
J. Sound Vib.
,
206
(
3
), pp.
287
308
.
41.
Kokkorakis
,
G. C.
, and
Roumeliotis
,
J. A.
,
1998
, “
Acoustic Eigenfrequencies in Concentric Spheroidal–Spherical Cavities: Calculation by Shape Perturbation
,”
J. Sound Vib.
,
212
(
2
), pp.
337
355
.
42.
Hasheminejad
,
S. M.
, and
Sanaei
,
R.
,
2007
, “
Ultrasonic Scattering by a Spheroidal Suspension Including Dissipative Effects
,”
J. Dispersion Sci. Technol.
,
28
(
7
), pp.
1093
1107
.
43.
Gong
,
Z.
,
Li
,
W.
,
Mitri
,
F. G.
,
Chai
,
Y.
, and
Zhao
,
Y.
,
2016
, “
Arbitrary Scattering of an Acoustical Bessel Beam by a Rigid Spheroid With Large Aspect-Ratio
,”
J. Sound Vib.
,
383
, pp.
233
247
.
44.
Zouros
,
G. P.
,
2014
, “
Exact Eigenfrequencies in Concentric Prolate Spheroidal-Spherical Metallic Cavities
,”
IEEE Microwave Wireless Compon. Lett.
,
24
(
12
), pp.
821
823
.
45.
Zouros
,
G. P.
,
Kotsis
,
A. D.
, and
Roumeliotis
,
J. A.
,
2015
, “
Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids
,”
IEEE Trans. Microwave Theory Tech.
,
63
(
3
), pp.
864
876
.
46.
Dorrington
,
G. E.
,
2006
, “
Drag of Spheroid-Cone Shaped Airship
,”
J. Aircr.
,
43
(
2
), pp.
363
371
.
47.
Kingan
,
M. J.
, and
Self
,
R. H.
,
2012
, “
Open Rotor Tone Scattering
,”
J. Sound Vib.
,
331
(
8
), pp.
1806
1828
.
48.
Lu
,
H. Y.
,
1990
, “
Fuselage Boundary-Layer Effects on Sound Propagation and Scattering
,”
AIAA J.
,
28
(
7
), pp.
1180
1186
.
49.
Wei
,
Y.
,
Shen
,
Y.
,
Jin
,
S.
,
Hu
,
P.
,
Lan
,
R.
,
Zhuang
,
S.
, and
Liu
,
D.
,
2016
, “
Scattering Effect of Submarine Hull on Propeller Non-Cavitation Noise
,”
J. Sound Vib.
,
370
, pp.
319
335
.
50.
Cao
,
X. T.
,
Hua
,
H. X.
, and
Zhang
,
Z. Y.
,
2011
, “
Sound Radiation From Shear Deformable Stiffened Laminated Plates
,”
J. Sound Vib.
,
330
(
16
), pp.
4047
4063
.
51.
Cao
,
X. T.
,
Hua
,
H. X.
, and
Ma
,
C.
,
2012
, “
Acoustic Radiation From Shear Deformable Stiffened Laminated Cylindrical Shells
,”
J. Sound Vib.
,
331
(
3
), pp.
651
670
.
52.
Falloon
,
P. E.
,
2001
, “Theory and Computation of Spheroidal Harmonics With General Arguments,”
Master's thesis
, The University of Western Australia, Perth, Australia.
53.
Flammer
,
C.
,
2005
,
Spheroidal Wave Functions
,
Dover Publications
,
Mineola, NY
.
54.
Ivanov
,
Y. A.
,
1968
, “Diffraction of Electromagnetic Waves on Two Bodies,” National Aeronautics and Space Administration, Washington, DC, NASA Technical Translation No. NASA-TT-F597.
55.
Zhang
,
S. J.
, and
Jin
,
J. M.
,
1996
,
Computation of Special Functions
,
Wiley
,
New York
.
You do not currently have access to this content.