Research Papers

Modeling and Experimental Investigation of a Helmholtz Resonator With a Flexible Plate

[+] Author and Article Information
Shahin S. Nudehi

Assistant Professor
e-mail: shahin.nudehi@valpo.edu

G. Scott Duncan

Associate Professor
e-mail: scott.duncan@valpo.edu
Mechanical Engineering Department,
Valparaiso University,
Valparaiso, IN 46383

Umar Farooq

Eaton Corporation,
2425 W. Michigan Ave.,
Jackson, MI 49202
e-mail: umarfarooq@eaton.com

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 10, 2011; final manuscript received January 27, 2013; published online June 6, 2013. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 135(4), 041102 (Jun 06, 2013) (6 pages) Paper No: VIB-11-1104; doi: 10.1115/1.4023810 History: Received May 10, 2011; Revised January 27, 2013

A Helmholtz resonator with a uniform, flexible end plate is studied in this work. This work shows that the flexible plate modifies the frequency response characteristics of the resonator, providing multiple distinct resonant frequencies instead of a single resonant frequency. Therefore, acoustical transmission loss will increase at each of the multiple resonant frequencies of the resonator and plate assembly versus at a single frequency for the unmodified Helmholtz resonator. By using receptance coupling as the modeling approach, the receptance of the Helmholtz resonator and flexible plate assembly is predicted by coupling receptance models of an unmodified Helmholtz resonator and a clamped plate. Finally, the predicted receptance of the Helmholtz resonator and flexible plate assembly is compared against experimental results.

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Helmholtz, H. V., 1912, On the Sensation of Tone as a Physiological Basis for the Theory of Music, 4th ed., Longmans, Green, London.
Rayleigh, J. W. S., 1877, The Theory of Sound, Macmillan, New York.
Howe, M., 1976, “On the Helmholtz Resonator,” J. Sound Vib., 45(3), pp. 427–440. [CrossRef]
Anderson, J., 1977, “The Effect of an Air Flow on a Single Side Branch Helmholtz Resonator in a Circular Duct,” J. Sound Vib., 52(3), pp. 423–431. [CrossRef]
Fahy, F. J., and Schofield, C., 1980, “A Note on the Interaction Between a Helmholtz Resonator and an Acoustic Mode of an Enclosure,” J. Sound Vib., 72(3), pp. 365–378. [CrossRef]
Temkin, S., 1981, Elements of Acoustics, Wiley, New York.
Hersh, A. S., and Tso, J., 1992, “Extended Frequency Range Helmholtz Resonator,” US Patent No. 5 119,427.
deBedout, J. M., Francheck, M. A., Bernhard, R. J., and Mongeau, L., 1997, “Adaptive-Passive Noise Control With Self-Tuning Helmholtz Resonators,” J. Sound Vib., 202(1), pp. 109–123. [CrossRef]
Birdsong, C., 1999, “A Semi-Active Helmholtz Resonator,” Ph.D. thesis, Michigan State University, East Lansing, MI.
Horowitz, S. B., Nishida, T., Cattafesta, L. N., and Sheplak, M., 2002, “Characterization of a Compliant-Backplate Helmholtz Resonator for an Electromechanical Acoustic Liner,” Int. J. Aeroacoust., 1(2), pp. 183–205. [CrossRef]
Birdsong, C., and Radcliffe, C., 1997, “A Smart Helmholtz Resonator,” International Mechanical Engineering Congress and Exposition-Active Noise Control, Dallas, TX, November.
Kostek, T., and Franchek, M., 2000, “Hybrid Noise Control in Ducts,” J. Sound Vib., 237(1), pp. 81–100. [CrossRef]
Singh, S., Howard, C., and Hansen, C., 2006, “Tuning a Semi-Active Helmholtz Resonator,” 6th International Symposium on Active Noise and Vibration Control (ACTIVE 2006), Adelaide, Australia, September 18–20.
Koopman, G., and Neise, W., 1982, “The Use of Resonators to Silence Centrifugal Blowers,” J. Sound Vib., 82, pp. 17–27. [CrossRef]
Chen, K. T., Chen, Y. H., Lin, K. Y., and Weng, C. C., 1998, “The Improvement on the Transmission Loss of a Duct by Adding Helmholtz Resonators,” Appl. Acoust., 54(1), pp. 71–82. [CrossRef]
Estve, S. J., and Johnson, M. E., 2005, “Adaptive Helmholtz Resonators and Passive Vibration Absorbers for Cylinder Interior Noise Control,” J. Sound Vib., 288(4-5), pp. 1105–1130. [CrossRef]
Selamat, A., and Lee, I., 2003, “Helmholtz Resonator With Extended Neck,” J. Acoust. Soc. Am., 113(41), pp. 1975–1985. [CrossRef] [PubMed]
Sugimoto, N., Masuda, M., and Hashiguchi, T., 2003, “Frequency Response of Nonlinear Oscillations of Air Column in a Tube With an Array of Helmholtz Resonators,” J. Acoust. Soc. Am., 114(4), pp. 1772–1784. [CrossRef] [PubMed]
Kim, S., Kim, Y.-H., and Jang, J.-H., 2006, “A Theoretical Model to Predict the Low-Frequency Sound Absorption of a Helmholtz Resonator Array,” J. Acoust. Soc. Am., 119(4), pp. 1933–1936. [CrossRef] [PubMed]
Farooq, U., and Nudehi, S. S., 2007, “A Nonlinear Acoustic Resonator,” ASME International Design Engineering Technical Conferences, 21st Biennial Conference on Mechanical Vibration and Noise (IDETC/CIE 2007), Las Vegas, NV, September 4–7, ASME Paper No. DETC2007-34700. [CrossRef]
Liu, F., Phipps, A., and Horowitz, S. B., 2008, “Acoustic Energy Harvesting Using an Electromechanical Helmholtz Resonator,” J. Acoust. Soc. Am., 123(4), pp. 1983–1990. [CrossRef] [PubMed]
Horowitz, S., Nishida, T., Cattafesta, III, L., and Sheplak, M., 2000, “Compliant-Backplate Helmholtz Resonators,” J. Acoust. Soc. Am., 107, pp. 2824. [CrossRef]
Bishop, R., and Johnson, D., 1979, The Mechanics of Vibration, Cambridge University Press, Cambridge, England.
Hurty, W., 1965, “Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Klosterman, A., and Lemon, J., 1972, “Dynamic Design Analysis Via the Building Block Approach,” Shock Vib. Bull., 42, pp. 97–104.
Duncan, G., Tummond, M., and Schmitz, T., 2005, “An Investigation of the Dynamic Absorber Effect in High-Speed Machining,” Int. J. Mach. Tools Manuf., 45(4-5), pp. 497–507. [CrossRef]
Rao, S. S., 2007, Vibration of Continuous Systems, Wiley, New York.
Meirovitch, L., 1996, Principles and Techniques of Vibrations, Prentice-Hall, Englewood Cliffs, NJ.
Pierce, A. D., 1989, Acoustics: An Introduction to Its Physical Principles and Applications, Acoustical Society of America, Springer-Verlag, New York.
Balachandran, B., and Magrab, E. B., 2009, Vibrations, 2nd ed., CL-Engineering, Toronto.
Greenwood, N., and Earnshaw, A., 1997, Chemistry of the Elements, 2nd ed., Butterworth-Heinemann, Burlington, MA.
Garrelick, J. M., 1979, “The Transmission Loss of a Wall Incorporating an Array of Resonators,” J. Acoust. Soc. Am., 65(1), p. S52. [CrossRef]
Prydz, R. A., Wirt, L. S., and Kuntz, H. L., 1990, “Transmission Loss of a Multilayer Panel With Internal Tuned Helmholtz Resonators,” J. Acoust. Soc. Am., 87, pp. 1597–1602. [CrossRef]
Davis, D., Stokes, G., Moore, D., and Stevens, G., 1954, “Theoretical and Experimental Investigation of Mufflers With Comments on Engine-Exhaust Muffler Design,” NASA Report No. 1192.
Rao, S., and Rao, S., 1995, Mechanical Vibrations, Addison-Wesley, Reading, MA.


Grahic Jump Location
Fig. 1

Assembly with two subsystems B and C

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Fig. 2

Schematic of a Helmholtz resonator

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Fig. 3

Schematic of the Helmholtz resonator with a flexible end plate

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Fig. 4

Predicted receptance results

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Fig. 5

Predicted transmission loss results

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Fig. 6

Experimental setup

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Fig. 7

Experimental and predicted results of unmodified Helmholtz resonator receptance

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Fig. 8

Experimental and simulation results of Helmholtz resonator with flexible end plate receptance



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