View
213
Download
0
Category
Preview:
Citation preview
References
[1] R. J. Bernhard, H. R. Hall, and J. D. Jones. Adaptive-passive noise control. In
Inter-noise 92, pages 427–430, 1992.
[2] R. J. Bernhard. The state of the art of active-passive noise control. In Joseph M.
Cuschieri, Stewart A. L. Glegg, and David M. Yeager, editors, Proceedings of
Noise-Con 94, pages 421–428. Fort Lauderdale, Florida, May 1994.
[3] L. J. Eriksson and M. T. Zuroski. From passive to active: a family of silencing
possibilities. In Proceedings of Noise-Con 97, pages 71–80, 1997.
[4] C. H. Hansen, C. Q. Howard, K. A. Burgemeister, and B. S. Cazzolato. Practical
implementaion of an active control system in a hot stack. In Proceedings of the
Australian Acoustical Society Conference, 1996.
[5] X. Li, X. Qiu, D. J. J. Leclercq, A. C. Zander, and C. H. Hansen. Implementation of
active noise control in a multi-modal spray dryer exhaust stack. Applied Acoustics,
67(1):28–48, 2006.
[6] J. W. S. Rayleigh. Theory of Sound. MacMillan and Company, 1940.
[7] R. L. Panton and J. M. Miller. Resonant frequencies of cylindrical Helmholtz
resonators. Journal of the Acoustical Society of America, 57(6):1533–1535, 1975.
[8] D. Li. Vibroacoustic behaviour and noise control studies of advanced composite
structures. PhD thesis, University of Pittsburgh, 2003.
191
REFERENCES
[9] H. von Helmholtz. Theorie der Luftschwingungen in Rohren mit offenen Enden.
Crelle, 1860.
[10] L. L. Beranek and I. L. Ver. Noise and Vibration Control Engineering. John Wiley
& Sons, 1992.
[11] D. A. Bies and C. H. Hansen. Engineering Noise Control. Spon Press, Third
edition, 2003.
[12] A. D. Pierce. Acoustics. The Acoustical Society of America, 1989.
[13] U. Ingard. On the theory and design of acoustic resonators. Journal of the Acous-
tical Society of America, 25(6):1037–1061, 1953.
[14] U. Ingard. The near field of a Helmholtz resonator exposed to a plane wave.
Journal of the Acoustical Society of America, 25(6), November 1953.
[15] U. Ingard and R. H. Lyon. The impedance of a resistance loaded Helmholtz
resonator. Journal of the Acoustical Society of America, 25(5), September 1953.
[16] M. Alster. Improved calculations for resonant frequencies of Helmholtz resonators.
Journal of Sound and Vibration, 24(1):63–85, 1972.
[17] P. K. Tang and W. A. Sirignano. Theory of a generalised Helmholtz resonator.
Journal of Sound and Vibration, 26(2):247–262, 1973.
[18] R. C. Chanaud. Effects of geometry on the resonance frequency of Helmholtz
resonators. Journal of Sound and Vibration, 178(3):337–348, 1994.
[19] R. C. Chanaud. Effects of geometry on the resonance frequency of Helmholtz
resonators, part II. Journal of Sound and Vibration, 204(5):829–834, 1997.
[20] A. Selamet, N. S. Dickey, and J. M. Novak. Theoretical, computational and
experimental investigation of Helmholtz resonators with fixed volume: Lumped
versus distributed analysis. Journal of Sound and Vibration, 187(2):358–367, 1995.
192
REFERENCES
[21] N. S. Dickey and A. Selamet. Helmholtz resonators: one-dimensional limit
for small cavity length-to-diameter ratios. Journal of Sound and Vibration,
195(3):512–517, 1996.
[22] A. Selamet, P. M. Radavich, N. S. Dickey, and J. M. Novak. Circular concentric
Helmholtz resonators. Journal of the Acoustical Society of America, 101(1):41–51,
January 1997.
[23] A. Selamet and Z. L. Ji. Circular asymmetric Helmholtz resonator. Journal of the
Acoustical Society of America, 107(5):2360–2369, may 2000.
[24] A. Selamet and I. Lee. Helmholtz resonator with extended neck. Journal of the
Acoustical Society of America, 113(4):1975–1985, April 2003.
[25] L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders. Fundamentals of
Acoustics. John Wiley & Sons, Third edition, 1982.
[26] M. L. Munjal. Acoustics of ducts and mufflers. John Wiley & Sons, 1987.
[27] J. W. Miles. The analysis of plane discontinuties in cylindrical tubes. Part I and
Part II. Journal of the Acoustical Society of America, 17(3):259–284, January
1946.
[28] F. C. Karal. The analogous acoustical impedance for discontinuties and constric-
tions of circular cross section. Journal of the Acoustical Society of America, 25,
327-334.
[29] A. D. Sahasrabudhe, M. L. Munjal, and S. Anantha Ramu. Analysis of interface
due to the higher order mode effects in a sudden area discontinuity. Journal of
Sound and Vibration, 185(3):515–529, 1995.
[30] A. Onorati. Prediction of the acoustical performances of muffling pipe systems by
the method of characteristics. Journal of Sound and Vibration, 171(3):369–395,
1994.
193
REFERENCES
[31] Z. L. Ji. Acoustic length correction of a closed cylindrical side-branched tube.
Journal of Sound and Vibration, 283:1180–1186, 2005.
[32] M. G. Prasad and M. J. Crocker. Insertion loss studies on models of automotive
exhaust systems. Journal of Acoustical Society of America, 70(1981):1339–1344,
November 1981.
[33] D. D. Davis, G. M. Stokes, D. Moore, and G. L. Stevens. Theoretical and experi-
mental investigation of mufflers with comments on engine-exhaust muffler design.
Technical report, NACA Annual Report, 1954.
[34] K. T. Chen, Y. H. Chen, K. Y. Lin, and C. C. Weng. The improvement on the
transmission loss of a duct by adding Helmholtz resonators. Applied Acoustics,
54(1):71–82, 1998.
[35] C. R. Fuller, J. P. Maillard, M. Mercadal, and A. H. von Flotow. Control of aircraft
interior noise using globally detuned vibration absorbers. Journal of Sound and
Vibration, 203(5):745–761, 1997.
[36] J. P. Carneal, F. Charette, and C. R. Fuller. Minimization of sound radiation from
plates using adaptive tuned vibration absorbers. Journal of Sound and Vibration,
270:781–792, 2004.
[37] J. Y. Chung and D. A. Blaser. Transfer function method for measuring in-duct
acoustic properties. I. Theory, II. Experiments. Journal of the Acoustical Society
of America, 68(3):907–921, 1980.
[38] A. F. Seybert and D. F. Ross. Experimental determination of acoustic properties
using a two-microphone random-excitation technique. Journal of the Acoustical
Society of America, 61(5):1362–1370, May 1977.
[39] ASTM International E 1050 98 - Standard test method for impedance and absorp-
tion of acoustic material using a tube, two microphones and a digital frequency
analysis system.
194
REFERENCES
[40] ISO 10534-1:1996 Acoustics - Determination of sound absorption coefficient and
impedance in impedance tubes - Part 1: Method using standing wave ratio.
[41] ISO 10534-2:1996 Acoustics - Determination of sound absorption coefficient and
impedance in impedance tubes - Part 2: Transfer-function method.
[42] M. Åbom. Modal decomposition in ducts based on transfer function measurements
between microphone pairs. Journal of Sound and Vibration, 135(1):95–114, 1989.
[43] G. Krishnappa. Cross-spectral method of measuring acoustic intensity by correct-
ing phase and gain mismatch errors by microphone calibration. Journal of the
Acoustical Society of America, 69(1):307–310, January 1981.
[44] J. Y. Chung. Cross-spectral method of measuring acoustic intensity without er-
ror caused by instrument phase mismatch. Journal of the Acoustical Society of
America, 64(6):1613–1616, December 1978.
[45] A. F. Seybert and D. K. Graves. Measurement of phase mismatch between two
microphones. In Proceedings of Noise-Con 85, pages 423–428. The Ohio State
University, June 3-5 1985.
[46] H. Bodén and M. Åbom. Influence of errors on the two-microphone method for
measuring acoustic properties in ducts. Journal of the Acoustic Society of America,
79(2):541–549, February 1986.
[47] W. T. Chu. Extension of the two-microphone transfer function method for
impedance tube measurements. Journal of the Acoustic Society of America,
80(1):347–348, July 1986.
[48] M. Åbom and H. Bodén. Error analysis of two-microphone measurements in ducts
with flow. Journal of the Acoustic Society of America, 83(6):2429–2438, June 1988.
195
REFERENCES
[49] E. Meyer, F. Mechel, and G. Kurtez. Experiments on the influence of flow on sound
attenuation in absorbing ducts. Journal of the Acoustical Society of America,
30(3):165–174, March 1958.
[50] J. S. Anderson. The effect of an air flow on a single side branch Helmholtz resonator
in a circular duct. Journal of Sound and Vibration, 52(3):423–431, June 1977.
[51] R. L. Panton and J. M. Miller. Excitation of a Helmholtz resonator by a turbulent
boundary layer. Journal of the Acoustical Society of America, 58(4):800–806,
October 1975.
[52] C. O. Paschereit, W. Weisenstein, P. Flohr, and W. Polifke. Apparatus for damp-
ing acoustic vibrations in a combustor. United States Patent Number 6,634,457,
2003.
[53] G. Kudernatsch. Exhaust gas system with Helmholtz resonator. United States
Patent Number 6,705,428, 2004.
[54] C. Q. Howard, B. S. Cazzolato, and C. H. Hansen. Exhaust stack silencer design
using finite element analysis. Noise Control Engineering Journal, 48(4):113–120,
2000.
[55] C. Q. Howard, C. H. Hansen, and A. Zander. Vibro-acoustic noise control treat-
ments for payloa bays of launch vehicles: Discrete to fuzzy solutions. Applied
Acoustics, 66:1235–1261, 2005.
[56] S. J. Estève. Control of sound transmission into payload fairings using distributed
vibration absorbers and Helmholtz resonators. PhD thesis, Virginia Polytechnic
Institute and State University, 2004.
[57] W. Neise and G. H. Koopmann. Reduction of centrifugal fan noise by use of
resonators. Journal of Sound and Vibration, 73:297–308, 1980.
196
REFERENCES
[58] G. Koopmann and W. Neise. The use of resonators to silence centrifugal blowers.
Journal of Sound and Vibration, 82:17–27, 1982.
[59] J. S. Lamancusa. An actively tuned, passive muffler system for engine silencing. In
Jiri Tichy and Sabih Hayek, editors, Proceedings of Noise-Con 87, pages 313–316.
The Pennsylvania State University, State College, Pennsylvania, June 1987.
[60] S. Sato and H. Matsuhisa. Semi-active noise control by a resonator with variable
parameters. In Proceedings of Inter-Noise 90, pages 1305–1308, 1990.
[61] H. Matsuhisa, B. Ren, and S. Sato. Semiactive control of duct noise by a volume-
variable resonator. Japan Society of Mechanical Engineers, International Journal,
35(2):223–228, 1992.
[62] J. M. de Bedout, M. A. Franchek, R. J. Bernhard, and L. Mongeau. Adaptive-
passive noise control with self-tuning Helmholtz resonators. Journal of Sound and
Vibration, 202(1):109–123, 1997.
[63] C. J. Radcliffe and C. Birdsong. An electronically tunable resonator for noise con-
trol. Society of Automotive Engineers, Noise & Vibration conference & Exposition,
2001.
[64] S. J. Estève and M. E. Johnson. Development of an adaptive Helmholtz res-
onator for broadband noise control. In Proceedings of IMECE 2004, Anaheim,
CA, November. 2004 ASME International Mechanical Engineering Congress.
[65] S. J. Estève and M. E. Johnson. Control of the noise transmitted into a cylinder
using optimally damped Helmholtz resonators and distributed vibration absorbers.
In Ninth International Congress on Sound and Vibration, pages 522–529. Orlando,
Florida, USA, July 2002.
[66] H. Kotera and S. Okhi. Resonator type silencer. United States Patent Number
5,5283,398, 1994.
197
REFERENCES
[67] I. R. McLean. Variably tuned Helmholtz resonator with linear response controller.
United States Patent Number 5,771,851, 1998.
[68] P. E. R. Stuart. Variable resonator. United States Patent Number 6,508,331, 2003.
[69] J. D. Kotsun, L. N. Goenka, D. J. Moenssen, and C. E. Shaw. Helmholtz resonator.
United States Patent Number 6,792,907, 2004.
[70] M. S. Ciray. Exhaust processor with variable tuning system. United States Patent
Number 6,915,876, 2005.
[71] C. W. S. To and A. G. Doige. A transient testing technique for the determination
of matrix parameters of acoustic systems, I: theory and principles. Journal of
Sound and Vibration, 62(2):207–222, 1978.
[72] C. W. S. To and A. G. Doige. A transient testing technique for the determination
of matrix parameters of acoustic systems, II: experimental procedures and results.
Journal of Sound and Vibration, 62(2):223–233, 1978.
[73] J C. Snowdon. Mechanical four pole parameters and their applications. Journal
of Sound and Vibration, 15(3):307–323, 1971.
[74] C. L. Morfey. Sound transmission and generation in ducts with flow. Journal of
Sound and Vibration, 14(1):37–55, 1971.
[75] R. D. Blevins. Formulas for natural frequency and mode shape. Krieger Publishing
Company, 2001.
[76] ANSYS Inc. ANSYS Release 9.0 Documentation.
[77] D. B. Woyak. Acoustics and Fluid-Structure Interaction. Swanson Analysis Sys-
tems, Inc, Houston.
[78] S. Imaoka. Acoustic elements and boundary conditions. http://www.ansys.net,
Memo number STI:05/01B, 2004.
198
REFERENCES
[79] P. L. Driesch. Active control in enclosures using optimally designed Helmholtz
resonators. PhD thesis, The Pennsylvania State University, Department of Me-
chanical and Nuclear Engineering, 2002.
[80] F. S. Tse, I. E. Morse, and R. T. Hinkle. Mechanical Vibrations Theory and
Applications. Allyn and Bacon Series in Mechanical Engineering and Applied
Mechanics. Allyn and Bacon, Inc., second edition, 1978.
199
This page intentionally contains only this sentence.
Appendix A
Transition of the Transfer Matrix
Method Elements and Sequence of the
State Variables Adopted For This
Study
As described in chapter 3, section 3.3.2.3, the transfer matrix of a circular duct of
uniform cross-sectional area S and length l, is given by [26]
pr
qr
=
cos(kl) jYr sin(kl)
j
Yr
sin(kl) cos(kl)
pr−1
qr−1
(A.1)
where,
Yr =c
Sis the characteristic impedance, and
k is the complex wave number.
pr, pr−1 and qr, qr−1 are the acoustic pressures and acoustic mass velocities at the
extreme ends of the duct, respectively (input and output sides). However, for this
201
study equation (A.1) was transformed to a different equation given below.
vr
pr
=
cos(kl) jS
ρcsin(kl)
jρc
Ssin(kl) cos(kl)
vr−1
pr−1
(A.2)
where vr and vr−1 represent acoustic volume velocities at input and output sides of
element r, respectively. This transformation was facilitated by relating acoustic volume
velocity and acoustic pressure instead of acoustic mass velocity and acoustic pressure
respectively. The theory behind the transition is shown below.
The acoustic mass velocity, qr is given by
q = Sρu (A.3)
where, u is the particle velocity and is given by
u =v
S(A.4)
Using the expressions for the acoustic mass and particle velocities, equations (A.3)
and (A.4), respectively in equation (A.1), one gets
pr
ρvr
=
cos(kl) jYr sin(kl)
j
Yr
sin(kl) cos(kl)
pr−1
ρvr−1
(A.5)
Substituting Yr =c
Sin equation (A.5), one gets
pr
ρvr
=
cos(kl) jc
Ssin(kl)
jS
csin(kl) cos(kl)
pr−1
ρvr−1
(A.6)
Multiplying the R.H.S. of equation (A.6), one gets
pr = cos(kl)pr−1 + jρc
Ssin(kl)vr−1 (A.7)
202
Appendix A. Transition of the Transfer Matrix Method Elements and Sequence of the State
Variables Adopted For This Study
ρvr = jS
csin(kl)pr−1 + ρ cos(kl)vr−1 (A.8)
Writing equations (A.7) and (A.8) in the matrix form, one gets
pr
vr
=
cos(kl) jρc
Ssin(kl)
jS
ρcsin(kl) cos(kl)
pr−1
vr−1
(A.9)
Inverting the sequence of state variables, acoustic pressure and volume velocity, in
equation (A.9) results in
vr
pr
=
cos(kl) jS
ρcsin(kl)
jρc
Ssin(kl) cos(kl)
vr−1
pr−1
(A.10)
203
This page intentionally contains only this sentence.
Appendix B
List of Symbols
a radius of the duct
a+, a−
modal amplitudes of acoustic pressure associated with the incident (positive
x direction) and reflected waves (negative x direction)
a [2×1] column vector containing the unknown modal amplitudes
Ac cross-sectional area of the cavity
An cross-sectional area of the opening
c speed of sound in the fluid medium
C damping coefficient
D cross-sectional perimeter of the duct which has the orifice drilled into its
wall
f1, f2 frequencies corresponding to the half-power points
fn resonance frequency of a SDOF system
fr resonance frequency of a HR (as a stand-alone device)
F forcing function
205
h either the orifice radius or viscous boundary layer thickness
H [2×1] column vector containing the transfer function between the two lo-
cations
k wave number
k complex wave number
k+n, k−n axial wave numbers in the positive and negative directions
K stiffness of the volume of the fluid in the cavity
l length of the duct
l0 end-correction of an unflanged open end of a duct
ln physical neck length of the HR
leff effective length of the neck
Lc length of the cavity
M effective mass of the fluid in the neck
M [2×2] modal matrix containing the propagation terms
n acoustic mode number
pe instantaneous acoustic pressure at the opening of the neck
pr, pr−1 acoustic pressures at the input side (source end) of the duct
p [2×1] column vector containing the measures of acoustic pressures at two
different locations
qr, qr−1 acoustic mass velocities at the output sides (open end) of the duct
Q quality factor of the duct-HR system
206
Appendix B. List of Symbols
r radius of the neck of the HR
R radius of the cavity of the HR
s microphone spacing
S cross-sectional area of the duct
t viscous boundary thickness
u acoustic particle velocity
vsp acoustic volume velocity of the loudspeaker
V volume of the HR
Vc volume of the cavity of the HR
Wnet in-duct net acoustic power transmission
Wnorm normalised in-duct net acoustic power transmission
x location along the duct
X amplitude of the frequency response of a SDOF system
Y characteristic impedance
Zl, Zr radiation impedance
Z0, Zs source impedance
−sign represents the propagation of acoustic wave in +ve x direction
+sign represents the propagation of acoustic wave in -ve x direction
β boundary admittance coefficient
ξ displacement of the fluid in the neck
ω angular excitation frequency
207
ζ critical damping ratio
φ phase of the frequency response of the SDOF system
ρ density of the fluid medium
Ψn eigenfunction for mode n
µ gas viscosity and for air, at 20oc, is equivalent to 1.8 × 10−5 kg m-1 s-1
γ ratio of specific heats and for air is equivalent to 1.4
ε either equal to 0 when the orifice or tube radiates into spaces of dimensions
� the wavelength of sound, or 0.5 when the orifice or tube radiates into
a free space without a flange, or 1 when the orifice or tube radiates into a
free space with a flange
208
Appendix C
Publications Originating from this
Thesis
209
Singh, S., Howard, C.Q. and Hansen, C.H. 2006: Tuning a semi-active Helmholtz resonator. ACTIVE 2006: Sixth International Symposium on Active Noise and Vibration Control, 18-20 September 2006, Adelaide Australia
NOTE: This publication is included in the print copy of the thesis held in the University of Adelaide Library.
Singh, S., Hansen, C.H. and Howard, C.Q. (2006): The elusive cost function for tuning adaptive Helmholtz resonators. Proceedings of Acoustics 2006: Noise of Progress, Clearwater Resort, Christchurch, New Zealand, 20-22 November, pp75-82
NOTE: This publication is included in the print copy of the thesis held in the University of Adelaide Library.
Recommended