Some experimental findings are presented on the effects of panel stiffness and receiving space absorption on low frequency sound transmission through panels into closed spaces. A simplified method for calculating the low frequency noise reduction of a cavity-backed panel is presented

Barton, C. K.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19770017963 2020-03-22T09:59:58+00:00Z
r^
x
a
a
z
NASA TECHNICAL	 NASA TM X- 73939
MEMORANDUM
r .
EXPERIMENTAL INVESTIGATION ON SOUND TRANSMISSION
THROUGH CAVITY-BACKED PANELS
By
C. Kearney Barton
June 1977
(NASA — T,M — X-73939)	 EXPERIMENTAL	 N77-24907
"VESTIGA.TION ON SOUND TP.ANSMISSION T3ROUGH
CAVITY — BACKED PANELS (NASA) 	 14 p HC A.02/MF
*_^ 1	 CSCL 20A	 Unclas
63/71	 29143
This info rmal documentation medium is used to provide accelerated or
special rt.:ease of technical information to selected users. The contents
may not meet NASA formal editing and publication standards, may be re-
vised, or may be incorporated in another publication.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
LANGLEY RESEARCH (ENTER, HAMPTON, VIRGINIA 23665
v
^`^~ JUN 1977	 '.^.
"' RECEIVED 	`-:
r J N ^,SF STI FACI A ITY	 ^ -
IN P61 BRANCH	
\:;^
I	 Netxnt No 2	 Government Access.on No 3.	 Recipient's Catalog No
NASA TM X-731x39
4	 Tale and Subtitle 5	 Report Date
.tune	 1977
EXPERIMENTAL INVESTIGATION ON SOUND TRANSMISSION 6	 Performmg Organization Code
THROUGH CAVITY-BACKED FANELS 2630
7	 A,,thorls) 8	 Performing Organization Report No
C.	 Kearney Barton _-__--
10	 Work Unit No.
505-09-13-019	 Per forrning Organization Name and Address
11	 Contract or Grant NoNASA Langley Research Center
Hampton, VA	 23665
13	 Type of Report and Period Covered
'technical Memorandum12	 Sponsoring Agency Name and Address
National Aeronautics and Space Administration 14	 Sponsoring Agency Code
Washington, DC	 20546
15.	 Supplementdry Notes
Presented at the 93rd Acoustical Society of Amcrica Meeting, June 7-10, 	 1977,
State College,	 PA.
16	 Abstract
A considerable amount of information has been developed in architectural 	 acoustics
on sound transmission through panels.
	
Emphasis has been on high-frequency transmission
where "mass law" is applicable and coincidence effects are important. 	 However,	 there
has been only limited attention given to low-frequency sound transmission. 	 Low-
frequency sound transmission is stiffness controlled in the frequency region below
structural resonances, and damping and stiffness controlled at resonances. 	 Furthermore,
the closed receiving room (cavity) behind the panel may have a significant effect on
the panel dynamics and, 	 therefore,	 the sound transmission.	 A panel backed by a closed
cavity provides a meaningful model for studying low-frequency sound transmission of the
type encountered in aircraft for example. 	 Although some theoretical work has been done
on the subject, only limited experimental data are available in the literature. 	 The
purpose of this paper is to present some experimental findings on the effects of panel
stiffness and receiving space absorption on low-frequency sound transmission through
panels into closed spaces.
	
In addition, a simplified method for calculating the low-
frequency noise reduction of a cavity-backed panel will be presented.
17	 Key Words (Suggested by Author(s)) 18	 Distribution Statement
panel stiffness
receiving space absorption Unclassified
low-frequency sound transmission
cavity-backed panel
71
-- Unlimited
19	 Security	 Classic (of this report) 20.	 Security Classif. (of this page) 21.	 No. of	 Pages	 22.	 Price'
Unclassified Unclassified 11	 $3.50
For sale by the National Technical Information Service Springfield, Virginia 22161
. ►.• r
l	 ..	 1	 -	 -
INTRODUCTION
A considerable amount of information has been developed in architec-
tural acoustics on sound transmission through panels, with empahsis on
middle and high frequencies where "mass law" and coincidence effects are
r
r
important. However, there has been only limited attention given to low-
!.	 frequency sound transmission, where stiffness, damping, and resonant
behavior are important. Furthermore, the receiving room behind the
panel may have a significant effect on the panel dynamics and, taerefore,
the sound transmission. A panel backed by a closed cavity provides a
meaningful model for studying low-frequency sound transmission of the
type encountered in light aircraft, for example.
The sound transmi_sLiion characteristics of a simple panel backed by
a closed, absorbent cavity are shown in figure 1. The measure of sound
transmission for this case is noise reduction (NR) and is expressed in
de • ibels as a function of frequency. The NR is the difference in
noise level (sound pressure level) across the panel. The frequency
range for convenience is broken up into four regions corresponding to
dominating physical mechanisms, as shown in the figure. The stiffness and
resonance regions represent the low-frequency portion of the frequency
range shown. As shown in figure 1, the noise reduction below the first
resonance is independent of frequency. This phenomenon has been studied
theoretically by several investigators (for example, references 1 2, 3).
However, very little data are available demonstrating this noise
reduction and also data are not available showing the transistion of
4
noise reduction from this stiffness region into the mass law region
(some data are available in references 3, 4, 5). In addition, the
theoretical work in references 1, 2, 3, 4 was for panels backed by hard-
walled cavities.
The purpose of this paper is to present experimental data showing
the effects of adding stiffness to a panel backed by a closed, absorbent
cavity, and to present a simple theory for predicting the noise reduction
for the stiffness, resonance, and mass regions of a panel backed by a
closed, absorbent cavity.
TEST APPARATUS
The test apparatus used in this study is shown in figure 2 and
consisted of a cavity raving high transmission loss on five sides, with
the sixth side left open for mounting test panels. The cavity was 30 cm
by 38 cm by 45 cm deep and was lined with 2.5 cm fiberglass on the sides
and 7.5 cm fiberglass on the cavity bottom.
The acoustic excitation was normally incident white noise provided
by two loudspeakers. The exterior noise level was determined by averaging
the outputs of two microphones near the panel surface in one-third octave
bands. Similarly, the inside noise level was determined by averaging
the outputs of two microphones in one-third octave bands. The noise
reduction was obtained by subtracting the average inside level from the
average outside level in each one-third octave band.
Three of the four test panels used in this study are shown in
figure 3. Each panel is 30 cm by 38 cm and each was clamped to the cavity.
The fourth panel (not shown in the figure) was lead-loaded vinyl having
2
the same surface density as the simple: panel shown in figure 3. The
three panels are each 0.79 mm thick aluminum. The only physical
differences in these panels is the stiffeners which were riveted onto
the panels as indicated in the figure. These three panels plus the
fourth (lead vinyl) represent a large variation in panel stiffness with
very little variation in panel mass (0.22 to 0.33 kg/m 2 ) and, thus,
provide a means for studying the effects of stiffness on noise reduction.
RESULTS
Experimental Data
The measured noise reduction for the four panels is shown in
figure 4. A calculated mass law curve for the simple alumintim panel is
included with each set of data for reference. The data show that adding
stiffness increases the noise reduction at frequencies below the
fundamental. The data also show that adding stiffness does not significantly
change the noise reduction above the first resonance. It is evident from
the data that only the fundamental mode has a significant effect on the
noise reduction. Finally, the data indicate that adding stiffeners to
the aluminw-n panels not only increased the frequency of the first mode,
but also reduced the severity of the resonance dip. The lead vinyl does
not follow this trend probably because of the very high internal damping
in the panel. The effects of damping will be discussed later in the paper.
Analytical Model
Because only one panel resonance appears in these experimental results,
a theoretical model using one panel mode seems in order. The model is
illustrated in figure 5. The model consists of a rigid, infinite panel
I^
I:
3
i	 f	 ----^.
supported on springs and backed by a wall having a frequency-dependent
impedance. There are no corrections for finir_e size effects such as
defraction. This model is analogous to that described in reference 6,
page 82, with the exception that the backing wall has impedance ZZ
instead of being a hard wall (Z Z -+ -).
The equation of motion and the corresponding equation for pressure
inside the cavity are shown in figure 5 as equation I. The variables
for a particular panel cavity system are frequency and the backing-wall
impedance. A simple, frequency-dependent expression for Z Z is needed
to complete the equation.
The impedance of fiberglass with a hard wall behind it is approxi-
mately pc (real.) at high frequencies. At low frequencies, the fiberglass
has virtually no e ff ect, so the wall impedance will approach infinity
(assumed real) as frequency goes to zero. Therefore a real, assumed
relationship for ZZ that varies from infinity at zero frequency to
Pc at high frequencies is appropriate. Such a relationship is given in
equation II.
It may be shown from equations I and II that for low frequencies,
the noise reduction becomes a function simply of panel and cavity stiffness
(independent of frequency as expected) as shown in equation 111. It may
be observed from this equation that doubling the panel natural frequency
may increase NR by up to 12 dB.
It may also be shown that, provided the first panel mode is lower
than the first depthwise acoustic mode, the system resonance can be
expressed as in equation IV, where it may be observed that the effect of
4
the cavity is simply to add a stiffness term to the stiffness of the
panel.
At high frequencies, the noise reduction reduces to mass law
(equation V) plus 6 dB for pressure doubling at the surface. This was
also expected because the absorbent cavity acts like an acoustic
termination at high frequencies since sound waves radiated by the panel
are not reflected back to the panel.
If the cavity impedance ( Zcavity) equals pc, equation I becomes 	 ^•
applicable to the transmission loss problem of reference 6, page 80,
except panel damping is included. It may be shown for this case that
the transmission loss (TL) at resonance can be expressed as in equation VI.
It may be observed from this equation that the TL at resonance increases
as much as 6 dB for a doubling of either damping ratio (C), natural
frequency (wn), or panel mass (m), provided the remaining two variables
(i.e., C, m, or (On) are held constant. Thus, by increasing the resonance
frequency, wn, (with constant m, C) the transmission loss at resonance 	 4
increases as well as the TL below resonance.
Using equations I and II of figure 5, the noise reduction was calculated
and plotted for each of the four panels used in the study. These calculations
are shown in figure 6 with the corresponding data for each panel. It may
be observed from the figure that the model provides a reasonable method
for calculating the noise reduction at low and mid-frequencies. It should
be noted that the prediction is poor for the aluminum panels at high fre-
quencies because coincidence effects are not included in the model and
5
C,
f
because the added mass of the stiffeners, although included in the
prediction model, is not uniformly distributed over the panel.
Conclusions drawn from the data presented in this report include:
(1) adding stiffness to a panel backed by a closed cavity increases the
noise reduction at frequencies below the first resonance, (2) additional
stiffness does not improve noise reduction at mid and high frequencies,
(3) for a random input and one-third octave band analysis, only the
first panel-cavity mode has a significant effect on the noise reduction,
(4) as the resonance frequency of Lite first panel-cavity mode was increased
with stiffeners for the aluminum panels, the noise reduction at the
resonance dip was increased, (5) the results of the simple analytical
model presented compared well with the data for the panels tested.
REFERENCES
1. Lyon, R. H.: Noise Reduction of Rectangular Enclosures with One
Flexible Wall. J. Acoust. Soc. Am., 3 5 (1963), pp. 1791-1797.
2. Bailey, J. Ronald and Hart, Franklin D.: :Noise Reduction Shape
Factors in the Low-Frequency Range. NASA CR-1155, Sept. 1968.
3. Dowell, E. H.: Acoustoelasticity. Princeton Univ. Report AMS
1280, May 1976. Work performed under NASA Grant NSG-1253.
4. Guy, R. W. and Bhattacharya, M. C.: The Transmission of Sound
Through a Cavity-Backed Finite Plate. J. Sound Vib., 27, (1973),
pp. 207-223.
5. Getline, G. L.: Low-Frequency Noise Reduction of lightweight
Airframe Structures. NASA CR-145104, 1976. Work performed
under NASA Contract NAS1-13910.
6. Richards, E. J. and Mead, D. J. (eds.): Noise and Acoustic Fatigue
in Aeronautics. John Wiley & Sons, Ltd., New York, 1968.
6
a^
t	 r	
_l	
r
rn
oz
ML C O n _
C=)	z
a ^
	-
m
mT G7-,^
z orn
zcn
TT	
^^
r•
00
G
n
r
n
CL
r•
n
rt
ro
a
0
r.
n
a
G
f^
rt
r•
O
O
O
n
n
w
w
rt
i
w
a
bCa
ro
w
O
n
rt
w
t
r•
rt
o►--+
P-
O
N
T
:L7
m
10
m
z
n
N
0w
M
;;o C/1
M C)
^^ D
z z
M
m
C7 D
cn
O cn
z
I0^
^ z
m
G7 _
O o
127 mG
n
M O^
Ln
mot.
_J
w
m
W	 r►..
0
W
J
QUh
Ln
O
U
Q
7
a^
ro
G
vi
r-
0
N
J
E
n
c
ro
v
^n
Gz
N
v
L+
7
00
L^.
V)
O =
70
<r- Q
m r
w
V)
Cr
_J
L.LJ
LL-0
C?
CY
a_
tLl
L!1
NAE IMAGE IS
OF POOR QUALITY
U)
rt
rt
cn
Lo
Cf)
H.
0
:s
rt
(D
In
rt
(D
F-
m
Cn
K
m
z
m
r-
,n
i
-n
m
z
M
0z
m
0 ^.
r1l
C)
0z
ORIGINAL, PAGE IS
OF POOR QUALITY
a
NNI I
O
to LL. J
Q Q
J
z_
Oti
I I
7
O	 O
Z l
w
(L/)	
m
Z oWw
O0
it
'c7	
NO
WJ
m (nJ ^ ^
E ° W IO
E ,^
00
Ln
8 N
S
U
C=> Z
O W
O'W
cl:f
I ( I L.L.
J V) F-J U O Z
Q z W W
- Z u
E U g
E C=) z
O° cs
o
m
W
>
p
O
O
M
O
G
0
u
L)
7
'O
v
0
G
GO
fA
41
G
w
w
u
m
w0
U)
Q)
w
w
v
ro
u
G
v
E
Q)
CL
x
w
i
v
on
w
E
i
8
^H
rE
I
:J
^E
IIliII
N^'
OOE
Nf"'^ N
00ow _+
^•rJF-'2J
r•
pi
(D
N
II
lr^^\.^N
rtIIx
rDHw
w.
rt
£ Cn +
W^
CL
C m~C
H
MO
n
w
r•
rr
Q• w
r
7v
r
Wn7vT IT I
rD
IIII11
<
.^•E
rtGWG Nw
N•tCGrD
IIrt^^I--^
r•
'DW^rtm
n^iWrt
N(D(AWH.
\wWnrn
rDrn
w
rD
IrD
W
cn
ro
0
---j
i
4'.
•
E
aE
Ay
Eo
ON
O(^N ..
W
'C
<W
ZN~'rta2b"O ^
liliIIIIIIII
N'ON.^ •O•
O^^N F Jr^ I N
E
ON
O+
n	z-
]
wW
N E+ I^.	^.
t7^ C
'CD--.3.
rt	I
W	N•N
^	^
ON
I
rt	+I 2'0	2^\r•
v vv ^ N`<
r.
HH
HH H
r.• f
{
ry
wz
LL-
V
C ^ ^J w
m
EE E OE °
DO
00
'
^o
^ N
UM
CD 
z
C7
N LL-CD
r--+
Ln
v
s^
ro
G
cr
v
a
x
u
bG
ro
ro
u
u
ro
G
ro
w
0
r-
0
co
.r.,
s^
ro
a
E0U
v
w
r--4
O
0
r--4
Of
w
_z
MC-T
c::)	 N
w
ZD —
Z V~
>
U
C:)
J	 <J
w
Q z o.
LLJ
o^	 , C\i
_	 < o
z0w -
^!' U m o 0 0 0 0
Z °w
Ckf
L	 I	 I I I	 I o
0 0 0 0 0
0
t	 ^


Experimental investigation on sound transmission through cavity-backed panels

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server