Research Papers

Modeling and Dynamic Analysis of an Electrical Helmholtz Resonator for Active Control of Resonant Noise

[+] Author and Article Information
Sang-Myeong Kim

Mechanical Engineering Department,
Ilha Solteira 15385-000, Brazil
e-mail: ksmnaver@naver.com

Joao A. Pereira

Mechanical Engineering Department,
Ilha Solteira 15385-000, Brazil
e-mail: japereira@dem.feis.unesp.br

Antonio E. Turra

Mechanical Engineering Department,
Ilha Solteira 15385-000, Brazil
e-mail: turra@dem.feis.unesp.br

Jun-Ho Cho

Department of Railway Transportation,
Woosong College,
59, Baekryong-ro,
Daejeon 34518, Korea
e-mail: jhcho@wsi.ac.kr

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 12, 2016; final manuscript received April 28, 2017; published online July 13, 2017. Assoc. Editor: Miao Yu.

J. Vib. Acoust 139(5), 051015 (Jul 13, 2017) (9 pages) Paper No: VIB-16-1541; doi: 10.1115/1.4036722 History: Received November 12, 2016; Revised April 28, 2017

This paper describes a theoretical and experimental investigation into an electrical Helmholtz resonator (EHR): that is, an active noise control (ANC) loudspeaker used in conjunction with a microphone and a feedback controller for suppressing resonant noise in an acoustic cavity. The microphone is collocated with the loudspeaker and a band pass filter of second-order is used as the control filter inside the controller. The EHR is configured as such in order to suppress an acoustic mode that is within the volume velocity drive frequency range of the loudspeaker used. The concepts of impedance and passivity are used to develop the mathematical model as well as to study its dynamics. From these, it is theoretically shown that the EHR for single-mode suppression is an extremely low-impedance acoustic damping device that electrically realizes the pressure neutralization mechanism of a conventional Helmholtz resonator (HR). Experimental work is also presented, in which an EHR is constructed to suppress the Helmholtz mode of an acoustic cavity at about 40 Hz by more than 40 dB, to justify the mathematical model and also to verify the dynamic control mechanism.

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Olson, H. F. , and May, E. G. , 1953, “ Electronic Sound Absorber,” J. Acoust. Soc. Am., 25(6), pp. 1130–1136. [CrossRef]
Clark, R. L. , and Cole, D. G. , 1995, “ Active Damping of Enclosed Sound Fields Through Direct Rate Feedback Control,” J. Acoust. Soc. Am., 97(3), pp. 1710–1716. [CrossRef]
Balas, M. J. , 1979, “ Direct Velocity Feedback Control of Large Space Structures,” J. Guid. Control, 2(3), pp. 252–253. [CrossRef]
Bisnette, J. B. , Smith, A. K. , Vipperman, J. S. , and Budny, D. D. , 2006, “ Active Noise Control Using Phase-Compensated, Damped Resonant Filters,” ASME J. Vib. Acoust., 128(2), pp. 148–155. [CrossRef]
Zhang, L. , Wu, L. , and Qiu, X. , 2013, “ An Intuitive Approach for Feedback Active Noise Controller Design,” Appl. Acoust., 74(1), pp. 160–168. [CrossRef]
Fanson, J. L. , and Caughey, T. K. , 1990, “ Positive Position Feedback Control for Large Space Structures,” AIAA J., 28(4), pp. 717–724. [CrossRef]
Kim, S. M. , Pietrzko, S. , and Brennan, M. J. , 2008, “ Active Vibration Isolation Using an Electrical Damper or an Electrical Dynamic Absorber,” IEEE Trans. Control Syst. Technol., 16(2), pp. 245–254. [CrossRef]
Kim, S. M. , Wang, S. , and Brennan, M. J. , 2011, “ Dynamic Analysis and Optimal Design of a Passive and an Active Piezo-Electrical Dynamic Vibration Absorber,” J. Sound Vib., 330(4), pp. 603–614. [CrossRef]
Kim, S. M. , Brennan, M. J. , and Abreu, G. L. C. M. , 2016, “ Narrowband Feedback for Narrowband Control of Resonant and Non-Resonant Vibration,” Mech. Syst. Signal Process., 76–77, pp. 47–57. [CrossRef]
Kinsler, L. E. , Frey, A. R. , Coppens, A. B. , and Danders, J. V. , 2000, Fundamentals of Acoustics, 4th ed., Wiley, New York, pp. 390–430.
Colloms, M. , and Darlington, P. , 2005, High Performance Loudspeakers, 6th ed., Wiley, Chichester, UK, pp. 27–44.
Fletcher, N. H. , 1992, Acoustic Systems in Biology, Oxford University Press, Oxford, UK, pp. 128–151.
De Bedout, J. M. , 1996, “ Adaptive-Passive Noise Control With Self-Tuning Helmholtz Resonators,” Ph.D. thesis, Purdue University, West Lafayette, IN. https://pdfs.semanticscholar.org/eae9/d5310d80a63cce084363fb9cddbb87f179a3.pdf
Kurdi, M. H. , Duncan, G. S. , and Nudehi, S. S. , 2014, “ Optimal Design of a Helmholtz Resonator With a Flexible End Plate,” ASME J. Vib. Acoust., 136(3), p. 031004. [CrossRef]
Birdsong, C. , and Radcliffe, C. , 2001, “ An Electronically Tunable Resonator for Noise Control,” SAE Technical Paper No. 2001-01-1615.
Zhang, Z. , Zhao, D. , Han, N. , Wang, S. , and Li, J. , 2015, “ Control of Combustion Instability With a Tunable Helmholtz Resonator,” Aerosp. Sci. Technol., 41, pp. 55–62. [CrossRef]
Fleming, A. J. , Niederberger, D. , Moheimani, S. O. R. , and Morari, M. , 2007, “ Control of Resonant Acoustic Sound Fields by Electrical Shunting of a Loudspeaker,” IEEE Trans. Control Syst. Technol., 15(4), pp. 689–703. [CrossRef]
Kim, S. M. , Pereira, J. A. , Lopes, V., Jr. , Turra, A. E. , and Brennan, M. J. , 2017, “ Practical Active Control of Cavity Noise Using Loop Shaping: Two Case Studies,” Appl. Acoust., 121, pp. 65–73. [CrossRef]
Cremer, L. , and Heckl, M. , 1988, Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies, 2nd ed., Springer-Verlag, Berlin, pp. 1–74; 406–425.
Kim, S. M. , and Brennan, M. J. , 1999, “ A Compact Matrix Formulation Using the Impedance and Mobility Approach for the Analysis of Structural-Acoustic Systems,” J. Sound Vib., 223(1), pp. 97–113. [CrossRef]
Anwar, A. , 2005, “ Low Frequency Finite Element Modeling of Passive Noise Attenuation in Ear Defenders,” M.Sc. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA. https://vtechworks.lib.vt.edu/handle/10919/31186
Rabinovich, A. B. , 2010, “ Seiches and Harbor Oscillations,” Handbook of Costal and Ocean Engineering, Y. C. Kim , ed., World Scientific Publishing Co., London, pp. 193–236.
Munjal, M. L. , 1987, Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design, Wiley, New York.
Studebaker, G. A. , and Zachman, T. A. , 1970, “ Investigation of the Acoustics of Earmold Vents,” J. Acoust. Soc. Am., 47, pp. 1107–1115. [CrossRef] [PubMed]
Boulandet, R. , and Lissek, H. , 2010, “ Optimization of Electroacoustic Absorbers by Means of Designed Experiments,” Appl. Acoust., 71(9), pp. 830–842. [CrossRef]
Byrnes, C. I. , Isidori, A. , and Willems, J. C. , 1991, “ Passivity, Feedback Equivalence, and the Global Stabilization of Minimum Phase Nonlinear Systems,” IEEE Trans. Autom. Control, 36(11), pp. 1228–1240. [CrossRef]
Kim, S. M. , 2015, “ Lumped Element Modeling of a Flexible Manipulator System,” IEEE/ASME Trans. Mechatronics, 20(2), pp. 967–974. [CrossRef]
Karnopp, D. , Crosby, M. J. , and Harwood, R. A. , 1974, “ Vibration Control Using Semi-Active Force Generators,” ASME J. Eng. Ind., 96(2), pp. 619–626. [CrossRef]
Birdsong, C. B. , and Radcliffe, C. J. , 1999, “ A Compensated Acoustic Actuator for Systems With Strong Dynamic Coupling,” ASME J. Vib. Acoust., 121(1), pp. 89–94. [CrossRef]


Grahic Jump Location
Fig. 1

Active noise control of an acoustic cavity using a microphone, a loudspeaker (source 2), and a controller −H(jω)

Grahic Jump Location
Fig. 4

Block diagram of the active system in Fig. 1

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Fig. 2

Impedance diagram of the active system in Fig. 1 under the assumption that H(jω) is a PBC

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Fig. 7

Measured (dashed–dotted and solid lines) and simulated (dashed) sound pressure responses before and after control (dBre: 20 μPa), when E1=0.1 V: (a) port 1 and (b) port 2. The symbol ○ is indicated at the target frequency 35 Hz.

Grahic Jump Location
Fig. 5

Experimental setup: a small cavity driven by the primary loudspeaker at port 1 and the control loudspeaker at port 2

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Fig. 6

Measured (solid lines) and simulated (dashed) plant responses: p2/E2. The frequency range Ω̃v is indicated by a thick line. (a) Bode plot (dBre: 20 μPa) and (b) Nyquist plot. The arrows in (b) indicate the direction of increasing frequency starting from a single arrow.

Grahic Jump Location
Fig. 10

Two auxiliary tests using the control loudspeaker: (a) diaphragm velocity measurement v and (b) the driving port acoustic impedance measurement Zcav=p/Q in which Q=Sv for the diaphragm area S

Grahic Jump Location
Fig. 8

Normalized measured acoustic impedance responses of the active and the passive loudspeaker in short circuit state compared with their simulation results. The symbols ▽ and ○ are indicated at 35 Hz.

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Fig. 3

Lumped-parameter models of the EHRs: (a) direct feedback control using Eq. (14) and (b) narrowband feedback control using Eq. (15)

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Fig. 9

Measured transmissibility responses TQ(jω) before (dashed–dotted) and after (solid) control, and TQ(jω)=−1 (dotted) for comparison. The symbols ▽ and ○ are indicated at 35 Hz.

Grahic Jump Location
Fig. 11

Measured (solid) and simulated (dashed) diaphragm velocity responses of the control loudspeaker. The frequency range Ω̃v is indicated by a thick line: (a) amplitude (dBre: 10−8m/s) and (b) Nyquist plot.

Grahic Jump Location
Fig. 12

Measured (solid lines) and simulated (dashed) driving port acoustic impedance responses: (a) amplitude and (b) Nyquist plot. The symbols, ○ and ▽, are, respectively, located at the Helmholtz and the fundamental natural frequency.




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