Research Papers

Optimal Design of a Helmholtz Resonator With a Flexible End Plate

[+] Author and Article Information
Mohammad H. Kurdi

Division of Business and Engineering,
Pennsylvania State University,
Altoona, PA 16601
e-mail: mhk13@psu.edu

G. Scott Duncan

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

Shahin S. Nudehi

Department of Mechanical Engineering,
Valparaiso University,
Valparaiso, IN 46383
e-mail: shahin.nudehi@valpo.edu

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 29, 2012; final manuscript received January 27, 2014; published online March 18, 2014. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 136(3), 031004 (Mar 18, 2014) (8 pages) Paper No: VIB-12-1365; doi: 10.1115/1.4026849 History: Received December 29, 2012; Revised January 27, 2014

This paper describes a design process that produces a small volume Helmholtz resonator capable of achieving high transmission loss across a desired frequency range. A multiobjective optimization formulation was used to design a Helmholtz resonator with a flexible end plate. The optimization formulation generated a Pareto curve of design solutions that quantify the trade-off between the optimization goals: minimum resonator volume and maximum transmission loss across a specified frequency range. The optimization problem was formulated and solved in the following manner. First, a mathematical formulation for the transmission loss of the Helmholtz resonator with a flexible plate was completed based on the resonator design parameters. Then, the weighted transmission loss across a specified frequency range and a minimum resonator volume were defined as optimization objectives. Finally, the Pareto curve of optimum design solutions was calculated using a gradient-based approach via the ɛ-constraint method. The optimization results allow the designer to select resonator design parameters that meet the requirements for both transmission loss and resonator volume. To validate the optimization results, two optimal Helmholtz resonators were manufactured and experimentally confirmed.

Copyright © 2014 by ASME
Topics: Design , Optimization
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Helmholtz, H., 1862, On the Sensations of Tone as a Physiological Basis for the Theory of Sound, Longmans Green and Co., London.
Sun, J., Jolly, M., and Norris, M., 1995, “Passive, Adaptive and Active Tuned Vibration Absorbers: A Survey,” ASME J. Mech. Des., 117(B), pp. 234–242. [CrossRef]
Zeninari, V., Kapitanov, V., Courtois, D., and Ponomarev, Y., 1999, “Design and Characteristics of a Differential Helmholtz Resonant Photoacoustic Cell for Infrared Gas Detection,” Infrared Phys. Tech., 40(1), pp. 1–23. [CrossRef]
Zhao, D., A'Barrow, C., Morgans, A., and Carrotte, J., 2009, “Acoustic Damping of a Helmholtz Resonator With an Oscillating Volume,” AIAA J., 47(7), pp. 1672–1679. [CrossRef]
Liu, F., Phipps, A., Horowitz, S., Khai, N., Cattafesta, L., Nishida, T., and Sheplak, M., 2008, “Acoustic Energy Harvesting Using an Electromechanical Helmholtz Resonator,” J. Acoust. Soc. Am., 123(4), pp. 1983–1990. [CrossRef] [PubMed]
Davis, D., Stokes, G., Moore, D., and Stevens, G., 1954, “Theoretical and Experimental Investigation of Mufflers With Comments on Engine-Exhaust Muffler Design,” National Advisory Committee for Aeronautics, NACA Report No. 1192.
Bielak, G. W., Premo, J. W., and Hersh, A. S., 1999, “Advanced Turbofan Duct Liner Concepts,” National Aeronautics and Space Administration, Report No. NASA/CR-1999-209002.
Tang, S., 2010, “On Sound Transmission Loss Across a Helmholtz Resonator in a Low Mach Number Flow Duct,” J. Acoust. Soc. Am., 127(6), pp. 3519–3525. [CrossRef] [PubMed]
Garrelick, J. M., 1979, “The Transmission Loss of a Wall Incorporating an Array of Resonators,” J. Acoust. Soc. Am., 65(S1), 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(4), pp. 1597–1602. [CrossRef]
Griffin, S., Lane, S., and Huybrechts, S., 2001, “Coupled Helmholtz Resonators for Acoustic Attenuation,” ASME J. Vib. Acoust., 123(1), pp. 11–17. [CrossRef]
Nudehi, S. S., Duncan, G. S., and Farooq, U., 2012, “Modeling and Experimental Investigation of a Helmholtz Resonator With a Flexible Plate,” ASME J. Vib. Acoust., 135(4), p. 041102. [CrossRef]
Farooq, U., and Nudehi, S., 2008, “A Nonlinear Acoustic Resonator,” ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, NV, September 4–7, ASME Paper No. DETC2007-34700, pp. 2015–2022. [CrossRef]
Horowitz, S., Nishida, T., Cattafesta, L., 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]
Li, D., and Cheng, L., 2007, “Acoustically Coupled Model of an Enclosure and a Helmholtz Resonator Array,” J. Sound Vib., 305(1–2), pp. 272–288. [CrossRef]
Unnikrishnan Nair, S., Shete, C., Subramoniam, A., Handoo, K., and Padmanabhan, C., 2010, “Experimental and Computational Investigation of Coupled Resonator-Cavity Systems,” Appl. Acoust., 71(1), pp. 61–67. [CrossRef]
Liu, F., Horowitz, S., Cattafesta, L., and Sheplak, M., 2006, “Optimization of an Electromechanical Helmholtz Resonator,” Aerospace Eng., 6250(352), pp. 1–12. [CrossRef]
Ingard, U., 1953, “On the Theory and Design of Acoustic Resonators,” J. Acoust. Soc. Am., 25(6), pp. 1037–1061. [CrossRef]
Henrique, L., Antunes, J., Inacio, O., and Paulino, J., 2005, “Application of Optimization Techniques for Acoustical Resonators,” Twelfth International Congress on Sound and Vibration (ICSV12), Lisbon, Portugal, July 11–14.
Inacio, O., Henrique, L., and Antunes, J., 2007, “Design of Duct Cross Sectional Areas in Bass-Trapping Resonators for Control Rooms,” Noise Contr. Eng. J., 55(2), pp. 172–182. [CrossRef]
Yu, G., 2009, “Acoustic Resonators for Noise Control in Enclosures: Modelling, Design and Optimization,” Ph.D. thesis, Hong Kong Polytechnic University, Hong Kong.
Liu, F., 2007, “A Tunable Electromechanical Helmholtz Resonator,” Ph.D. thesis, University of Florida, Gainesville, FL.
Papila, M., Haftka, R., Nishida, T., and Sheplak, M., 2006, “Piezoresistive Microphone Design Pareto Optimization: Tradeoff Between Sensitivity and Noise Floor,” J. MEMS, 15(6), pp. 1632–1943. [CrossRef]
Deb, K., 2001, Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, Hoboken, NJ.
Steuer, R. E., 1986, Multiple Criteria Optimization: Theory, Computation, and Application, John Wiley and Sons, Hoboken, NJ.
Chankong, V., and Haimes, Y. Y., 1983, Multi-Objective Decision Making: Theory and Methodology, North-Holland, Amsterdam.
Miettinen, K., 1999, Nonlinear Multi-Objective Optimization, Kluwer Academic, New York.
Kurdi, M., Beran, P., Stanford, B., and Snyder, S., 2009, “Optimal Actuation of Nonlinear Resonant Systems,” J. Struct. Multidisc. Optim., 41(1), pp. 65–86. [CrossRef]
Rao, S. S., 2007, Vibrations of Continuous Systems, John Wiley & Sons, Hoboken, NJ.
Temkin, S., 1981, Elements of Acoustics, John Wiley & Sons, Hoboken, NJ.
MathWorks, 2014, “MATLAB and Simulink for Technical Computing,” http://www.mathworks.com/
Selamet, A., Radavich, P., Dickey, N., and Novak, J., 1997, “Circular Concentric Helmholtz Resonators,” J. Acoust. Soc. Am., 101(1), pp. 41–51. [CrossRef]
Nowak, D., Bellucci, V., and Paschereit, C., 2001, “Numerical Prediction of the Natural Frequencies of the Helmholtz Resonator Coupled With Enclosure Cavity,” 2nd European Conference on Computational Mechanics (ECCM-2001), Cracow, Poland, June 26–29, pp. 850–851.
National Instruments, 2014, “Test, Measurement, and Embedded Systems,” http://www.ni.com/
Tao, Z., and Seybert, A., 2003, “A Review of Current Techniques for Measuring Muffler Transmission Loss,” SAE Technical Paper No. 2003-01-1653. [CrossRef]
Chung, J., and Blaser, D., 1980, “Transfer Function Method of Measuring In-Duct Acoustic Properties. I. Theory,” J. Acoust. Soc. Am., 68(3), pp. 907–913. [CrossRef]
Munjal, M., and Doige, A., 1990, “Theory of a Two Source-Location Method for Direct Experimental Evaluation of the Four-Pole Parameters of an Aeroacoustic Element,” J. Sound Vib., 141(2), pp. 323–333. [CrossRef]
Bishop, R., and Johnson, D., 2011, The Mechanics of Vibration, Cambridge University Press, Cambridge, UK.
Meirovitch, L., 1996, Principles and Techniques of Vibrations, Prentice-Hall, Upper Saddle River, NJ.


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Fig. 1

Schematic and subassemblies of a Helmholtz resonator with flexible plate

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Fig. 2

Pareto front (square markers present nondominated designs and circle markers represent dominated designs)

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Fig. 3

Constraint optimization of weighted TL and chamber volume (α = 1)

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Fig. 4

Trade-off curve with objective function adjusted to favor nominal desired frequency (α = 3)

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Fig. 5

Trade-off curve with objective function adjusted to favor nominal desired frequency (α = 3) and constraint on diameter ratio

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Fig. 6

Resonator experimental setup assembly mounted to an instrumented duct

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Fig. 7

Predicted and measured transmission loss for baseline design

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Fig. 8

Predicted transmission loss for optimal designs A and B with experimental measurement



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