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.