Technical Brief

Tailoring Plate Thickness of a Helmholtz Resonator for Improved Sound Attenuation

[+] Author and Article Information
Mohammad Kurdi

Power Transmission Division,
Lufkin Industries, LLC,
Part of GE Oil and Gas,
Wellsville, NY 14895
e-mail: mkurdi@ford.com

Shahin Nudehi

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

Gregory Scott Duncan

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

1Present address: Ford Motor Company, Dearborn, MI 48126.

2Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 16, 2018; final manuscript received January 2, 2019; published online February 13, 2019. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 141(3), 034502 (Feb 13, 2019) (5 pages) Paper No: VIB-18-1401; doi: 10.1115/1.4042519 History: Received September 16, 2018; Revised January 02, 2019

In this work, the transmission loss of a Helmholtz resonator is maximized (optimized) by allowing the resonator end plate thickness to vary for two cases: (1) a nonoptimized baseline resonator and (2) a resonator with a uniform flexible endplate that was previously optimized for transmission loss and resonator size. To accomplish this, receptance coupling techniques were used to couple a finite element model of a varying thickness resonator end plate to a mass-spring-damper model of the vibrating air mass in the resonator. Sequential quadratic programming was employed to complete a gradient-based optimization search. By allowing the end plate thickness to vary, the transmission loss of the nonoptimized baseline resonator was improved significantly, 28%. However, the transmission loss of the previously optimized resonator for transmission loss and resonator size showed minimal improvement.

Copyright © 2019 by ASME
Topics: Optimization , Design
Your Session has timed out. Please sign back in to continue.


Doaré, O. , Kergourlay, G. , and Sambuc, C. , 2013, “Design of a Circular Clamped Plate Excited by a Voice Coil and Piezoelectric Patches Used as a Loudspeaker,” ASME J. Vib. Acoust., 135(5), p. 051025. [CrossRef]
Duan, W. , Wang, C. M. , and Wang, C. , 2008, “Modification of Fundamental Vibration Modes of Circular Plates With Free Edges,” J. Sound Vib., 317(3–5), pp. 709–715. [CrossRef]
Peters, H. J. , Tiso, P. , Goosen, J. F. , and van Keulen, F. , “Control of the Eigensolutions of a Harmonically Driven Compliant Structure,” 4th ECCOMAS Thematic Conference onComputational Methods in Structural Dynamics and Earthquake Engineering, Kos Island, Greece, June 12–14, pp. 3536–3549.
Peters, H. , Tiso, P. , Goosen, J. , and van Keulen, F. , 2014, “A Modal-Based Approach for Optimal Active Modifications of Resonance Modes,” J. Sound Vib., 334, pp. 151–163. [CrossRef]
Auricchio, F. , and Taylor, R. , 1994, “A Shear Deformable Plate Element With an Exact Thin Limit,” Comput. Methods Appl. Mech. Eng., 118(3–4), pp. 393–412. [CrossRef]
Bishop, R. , and Johnson, D. , 2011, The Mechanics of Vibration, Cambridge University Press, Cambridge, UK.
Taylor, R. L. , 2014, “FEAP—Finite Element Analysis Program,” University of California, Berkeley, CA.
Schittkowski, K. , 2006, “NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm With Distributed and Non-Monotone Line Search-User's Guide, Version 2.2,” University of Bayreuth, Bayreu, Germany.
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]
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]
Davis, D. D. , Stokes, G. M. , Moore, D. , and Stevens, G. L. , 1954, Theoretical and Experimental Investigation of Mufflers With Comments on Engine-Exhaust Muffler Design, US Government Printing Office, Washington, DC.
Temkin, S. , and Temkin, S. , 1981, Elements of Acoustics, Wiley, New York.
Haftka, R. T. , and Gurdal, Z. , 1992, Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Cook, R. , Malkus, D. , Plesha, M. , and Witt, R. , 2002, Concepts and Applications of Finite Element Analysis, Wiley, New York.
Zienkiewicz, O. C. , and Taylor, R. L. , 2000, The Finite Element Method: The Basis, Vol. 1, Butterworth-Heinemann, Oxford, UK.


Grahic Jump Location
Fig. 1

Helmholtz resonator with a flexible plate: (a) geometric properties and (b) coordinates used in receptance assembly

Grahic Jump Location
Fig. 2

Optimization results of the baseline geometry: (a) block mesh: ΔTL = 8.89 dB and (b) blended mesh: ΔTL = 8.72 dB

Grahic Jump Location
Fig. 3

Optimization result for the baseline geometry (ΔTL = 9.08 dB)

Grahic Jump Location
Fig. 4

Optimization results of optimal design-1 geometry: (a) block mesh: ΔTL = 9.05 dB and (b) blended mesh: ΔTL = 10.48 dB



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In