Active control of the sound radiated from a piston set in a rigid sphere with a set of control point sources around is considered in this paper, where the scattering sound field of the control sound from the rigid sphere has been taken into account to minimize the total radiated sound power. Analytic results of the sound power are obtained and numerical simulations show that it is possible to reduce the radiation from a small piston set in a rigid sphere similar to the size of a human head up to a certain frequency. It is found that the introduction of the scattering object makes significant differences from the active control without scattering objects. This being the case, the scattering object makes the active noise control easier. To increase the global reduction of sound-power output, the optimal number and locations of the control sources and the optimal number and locations of error sensors are discussed. Finally, experiments with one control source and one error sensor around a head simulator have been carried out to verify the simulation results.

1.
P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic, New York, 1992).
2.
C. H. Hansen and S. D. Snyder, Active Control of Noise and Vibration (E&FN SPON, London, 1997).
3.
S. J. Elliott, Signal Processing for Active Control (Academic, London, 2001).
4.
S. M. Kuo and D. R. Morgan, Active Noise Control Systems: Algorithms and DSP Implementations (Wiley, New York, 1996).
5.
C. F. Ross, “Active control of sound,” Ph.D. thesis, University of Cambridge (1980).
6.
J.
Garcia-Bonito
and
S. J.
Elliott
, “
Local active control of diffracted diffuse sound fields
,”
J. Acoust. Soc. Am.
98
(
2
),
1017
1024
(
1995
).
7.
A.
David
and
S. J.
Elliott
, “
Numerical studies of actively generated quiet zones
,”
Appl. Acoust.
41
,
63
79
(
1994
).
8.
J.
Garcia-Bonito
,
S. J.
Elliott
, and
M.
Bonilha
, “
Active cancellation of pressure at a point in a pure-tone diffracted diffuse sound field
,”
J. Sound Vib.
201
(
1
),
43
65
(
1997
).
9.
J.
Garcia-Bonito
and
S. J.
Elliott
, “
Active cancellation of acoustic pressure and particle velocity in the near field of a source
,”
J. Sound Vib.
221
(
1
),
85
116
(
1999
).
10.
X.
Qiu
,
C. H.
Hansen
, and
X.
Li
, “
A comparison of near-field acoustic error sensing strategies for the active control of harmonic free-field sound radiation
,”
J. Sound Vib.
215
(
1
),
81
103
(
1998
).
11.
A.
Berry
,
X.
Qiu
, and
C. H.
Hansen
, “
Near-field sensing strategies for active control of the sound radiated from a plate
,”
J. Acoust. Soc. Am.
106
,
3394
3406
(
1999
).
12.
T.
Martin
and
A.
Roure
, “
Optimization of an active noise control system using spherical harmonic expansion of the primary field
,”
J. Sound Vib.
201
(
5
),
577
593
(
1997
).
13.
T.
Martin
and
A.
Roure
, “
Active noise control of acoustic sources using spherical harmonics expansion and a genetic algorithm: Simulation and experiment
,”
J. Sound Vib.
212
(
3
),
511
523
(
1998
).
14.
P. A.
Nelson
,
A. R. D.
Curtis
,
S. J.
Elliott
, and
A. J.
Bullmore
, “
The minimum power output of free-field point sources and the active control of sound
,”
J. Sound Vib.
116
(
3
),
397
414
(
1987
).
15.
C.
Deffayet
and
P. A.
Nelson
, “
Active control of low-frequency harmonic sound radiated by a finite panel
,”
J. Acoust. Soc. Am.
84
,
2192
2199
(
1988
).
16.
L.
Song
,
G. H.
Koopmann
, and
J. B.
Fahnline
, “
Active control of the acoustic radiation of a vibrating structure using a superposition formulation
,”
J. Acoust. Soc. Am.
89
(
6
),
2786
2792
(
1991
).
17.
G. H.
Koopmann
,
L.
Song
, and
J. B.
Fahnline
, “
A method for computing acoustic fields based on the principle of wave superposition
,”
J. Acoust. Soc. Am.
86
(
6
),
2433
2438
(
1989
).
18.
L.
Song
,
G. H.
Koopmann
, and
J. B.
Fahnline
, “
Numerical errors associated with the method of superposition for computing acoustic fields
,”
J. Acoust. Soc. Am.
89
(
6
),
2625
2633
(
1991
).
19.
M. E.
Johnson
,
S. J.
Elliott
,
K. H.
Baek
, and
J.
Garcia-Bonito
, “
An equivalent source technique for calculating the sound field inside an enclosure containing scattering objects
,”
J. Acoust. Soc. Am.
104
(
3
),
1221
1231
(
1998
).
20.
R.
Jeans
and
I. C.
Mathews
, “
The wave superposition method as a robust technique for computing acoustic fields
,”
J. Acoust. Soc. Am.
92
(
2
),
1156
1166
(
1992
).
21.
M.
Ochmann
, “
The source simulation technique for acoustic radiation problems
,”
Acoustica
81
,
512
527
(
1995
).
22.
P. A.
Nelson
and
Y.
Kahana
, “
Spherical harmonics, singular-value decomposition and the head-related transfer function
,”
J. Sound Vib.
239
(
4
),
607
637
(
2001
).
23.
R. O.
Duda
, “
Range dependence of the response of a spherical head model
,”
J. Acoust. Soc. Am.
104
(
5
),
3048
3058
(
1998
).
24.
D. S.
Brungart
and
W. M.
Rabinowitz
, “
Auditory localization of nearby sources. I. Head-related transfer functions
,”
J. Acoust. Soc. Am.
106
(
3
),
1465
1479
(
1999
).
25.
P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, Inc., 1968).
26.
C. Flammer, Spherical Wave Functions (Stanford University Press, Stanford, 1957).
27.
J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).
28.
D. T. Tsahalis, S. K. Katsikas, and D. A. Manolas, “A genetic algorithm for optimal positioning of actuators in active noise control: Results from the ASANCA project,” Inter-noise 93, 83–88 (1993).
29.
K. H.
Beak
and
S. J.
Elliott
, “
Natural algorithm for choosing source locations in active control systems
,”
J. Sound Vib.
186
(
2
),
245
267
(
1995
).
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