Abstract

As the importance of sound attenuation through weight-critical structures has grown and mass law based strategies have proven impractical, engineers have pursued alternative approaches for sound attenuation. Membrane-type acoustic metamaterials have demonstrated sound attenuation significantly higher than mass law predictions for narrow, tunable bandwidths. Similar phenomena can be achieved with plate-like structures. This paper presents an analytical model for the prediction of transmission loss through rectangular plates arbitrarily loaded with rigid masses, accommodating any combination of clamped and simply supported boundary conditions. Equations of motion are solved using a modal expansion approach, incorporating admissible eigenfunctions given by the natural mode shapes of single-span beams. The effective surface mass density is calculated and used to predict the transmission loss of low-frequency sound through the plate–mass structure. To validate the model, finite element results are compared against analytical predictions of modal behavior and shown to achieve agreement. The model is then used to explore the influence of various combinations of boundary conditions on the transmission loss properties of the structure, revealing that the symmetry of plate mounting conditions strongly affects transmission loss behavior and is a critical design parameter.

References

1.
Toyoda
,
M.
,
Kugo
,
H.
,
Shimizu
,
T.
, and
Takahashi
,
D.
,
2008
, “
Effects of an Air-Layer-Subdivision Technique on the Sound Transmission Through a Single Plate
,”
J. Acoust. Soc. Am.
,
123
(
2
), pp.
825
831
.
2.
Yang
,
Z.
,
Mei
,
J.
,
Yang
,
M.
,
Chan
,
N. H.
, and
Sheng
,
P.
,
2008
, “
Membrane-Type Acoustic Metamaterial With Negative Dynamic Mass
,”
Phys. Rev. Lett.
,
101
(
20
),
204301
.
3.
Liu
,
Z.
,
Zhang
,
X.
,
Mao
,
Y.
,
Zhu
,
Y. Y.
,
Yang
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
(
5485
), pp.
1734
1736
.
4.
Naify
,
C. J.
,
Chang
,
C. M.
,
McKnight
,
G.
, and
Nutt
,
S.
,
2010
, “
Transmission Loss and Dynamic Response of Membrane-Type Locally Resonant Acoustic Metamaterials
,”
J. Appl. Phys.
,
108
(
11
),
114905
.
5.
Zhang
,
Y.
,
Wen
,
J.
,
Xiao
,
Y.
,
Wen
,
X.
, and
Wang
,
J.
,
2012
, “
Theoretical Investigation of the Sound Attenuation of Membrane-Type Acoustic Metamaterials
,”
Phys. Lett. A
,
376
(
17
), pp.
1489
1494
.
6.
Naify
,
C. J.
,
Chang
,
C.
,
McKnight
,
G.
, and
Nutt
,
S.
,
2011
, “
Transmission Loss of Membrane-Type Acoustic Metamaterials With Coaxial Ring Masses
,”
J. Appl. Phys.
,
110
(
12
),
124903
.
7.
Naify
,
C. J.
,
Chang
,
C.-M.
,
McKnight
,
G.
, and
Nutt
,
S. R.
,
2012
, “
Scaling of Membrane-Type Locally Resonant Acoustic Metamaterial Arrays
,”
J. Acoust. Soc. Am.
,
132
(
4
), pp.
2784
2792
.
8.
Ingard
,
U.
,
1954
, “
Transmission of Sound Through a Stretched Membrane
,”
J. Acoust. Soc. Am.
,
26
(
1
), pp.
99
101
.
9.
Kornhauser
,
E. T.
, and
Mintzer
,
D.
,
1953
, “
On the Vibration of Mass-Loaded Membranes
,”
J. Acoust. Soc. Am.
,
25
(
5
), pp.
903
906
.
10.
Cohen
,
H.
, and
Handelman
,
G.
,
1957
, “
On the Vibration of a Circular Membrane With Added Mass
,”
J. Acoust. Soc. Am.
,
29
(
2
), pp.
229
233
.
11.
Chen
,
Y.
,
Huang
,
G.
,
Zhou
,
X.
,
Hu
,
G.
, and
Sun
,
C.-T.
,
2014
, “
Analytical Coupled Vibroacoustic Modeling of Membrane-Type Acoustic Metamaterials: Membrane Model
,”
J. Acoust. Soc. Am.
,
136
(
3
), pp.
969
979
.
12.
Langfeldt
,
F.
,
Gleine
,
W.
, and
von Estorff
,
O.
,
2015
, “
Analytical Model for Low-Frequency Transmission Loss Calculation of Membranes Loaded With Arbitrarily Shaped Masses
,”
J. Sound Vib.
,
349
, pp.
315
329
.
13.
Xin
,
F. X.
, and
Lu
,
T. J.
,
2009
, “
Analytical and Experimental Investigation on Transmission Loss of Clamped Double Panels: Implication of Boundary Effects
,”
J. Acoust. Soc. Am.
,
125
(
3
), pp.
1506
1517
.
14.
Kim
,
H.-S.
,
Kim
,
S.-R.
,
Lee
,
S.-H.
,
Seo
,
Y.-H.
, and
Ma
,
P.-S.
,
2016
, “
Sound Transmission Loss of Double Plates With an Air Cavity Between Them in a Rigid Duct
,”
J. Acoust. Soc. Am.
,
139
(
5
), pp.
2324
2333
.
15.
Chen
,
Y.
,
Huang
,
G.
,
Zhou
,
X.
,
Hu
,
G.
, and
Sun
,
C.-T.
,
2014
, “
Analytical Coupled Vibroacoustic Modeling of Membrane-Type Acoustic Metamaterials: Plate Model
,”
J. Acoust. Soc. Am.
,
136
(
6
), pp.
2926
2934
.
16.
Inman
,
D. J.
,
2014
,
Engineering Vibration
,
Pearson Education, Inc.
,
Upper Saddle River, NJ
.
17.
Fahy
,
F. J.
, and
Gardonio
,
P.
,
2007
,
Sound and Structural Vibration: Radiation, Transmission, and Response
,
Academic Press
,
Oxford, UK
.
18.
Belvins
,
R. D.
,
2016
,
Formulas for Dynamics, Acoustics, and Vibration
,
John Wiley & Sons, Ltd
,
Chichester, West Sussex
.
You do not currently have access to this content.