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.

References

1.
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
.
2.
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
.
3.
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.
4.
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
.
5.
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
.
6.
Bishop
,
R.
, and
Johnson
,
D.
,
2011
,
The Mechanics of Vibration
,
Cambridge University Press
, Cambridge, UK.
7.
Taylor
,
R. L.
,
2014
, “
FEAP—Finite Element Analysis Program
,” University of California, Berkeley, CA.
8.
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.
9.
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
.
10.
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
.
11.
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.
12.
Temkin
,
S.
, and
Temkin
,
S.
,
1981
,
Elements of Acoustics
,
Wiley
,
New York
.
13.
Haftka
,
R. T.
, and
Gurdal
,
Z.
,
1992
,
Elements of Structural Optimization
,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
.
14.
Cook
,
R.
,
Malkus
,
D.
,
Plesha
,
M.
, and
Witt
,
R.
,
2002
,
Concepts and Applications of Finite Element Analysis
,
Wiley
,
New York
.
15.
Zienkiewicz
,
O. C.
, and
Taylor
,
R. L.
,
2000
,
The Finite Element Method: The Basis
, Vol.
1
,
Butterworth-Heinemann
, Oxford, UK.
You do not currently have access to this content.