Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
105i351
The present invention relates to a sound absorb-
ing structure, and particularly a sound absorbing panel.
Various types of resonant sound absorbers have
been proposed heretofore for use in silencers or mufflers
S for gas turbine exhaust ducts and similar adverse environ-
mental installations. Also, so-called "pan-pipes" type of
structures have been proposed heretofore as sound absorbing
wall treatments for ducts carrying high velocity gases. The
pan-pipe structure comprises a plurality of resonators of
diminishing sizes, linearly disposed, to be resonant at var-
ious frequencies. While these prior devices may be classi-
fied as the same general type of absorber as the present in-
vention, namely multiple resonators, their performance is
inferior to that of the present invention for reasons that
will appear hereinafter.
There is also a honeycomb sandwich type of sound
absorption strucutre having an oblique resi~tive partition
disposed within each honeycomb cell. In the development of
this latter structure it was found that the computed imped-
ance p~ots correlated very closely with all empirical data80 long as the resistance of the oblique partition was near
optimum or below. However, it was found that beginning with
an acoustical resistance somewhat`above optimum, the analyti-
cal model failed to predict the experimental results. In
this high-resistance region, computer-derived predictions
indicated a potentially useful characteristic; namely, an
acoustic resistance which increases with frequency and a
reactance which rapidly approaches and remains at or near
zero. The simple analytical model, upon which th~e computer
program for producing the aforementioned impedance plots was
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lOSi351
based, assumed that the basic waveguide was subdivided into
a large number (namely, 100) of parallel waveguidelets, each
of which functions independently of the others. The total
admittance A is, then, the sum of the independent admittances
of the waveguidelets, each of which can ba computed from its
geometry by classical means.
Thus: A = n An An = z
Z = 1
Where: A = Acoustic admittance
n = Index num~er (0, 1, 2, 3, etc.)
Z = Acoustic Impedance
In accordance with the present invention it has
been found that experimental data can be made to yield the
above-mentioned desired characteristics by physically sub- ~
dividing the cell into 100 (or an appropriately large number ~ -
of) waveguidelets.
In the present invention there is disclosed a
sound absorptive structure comprising a two-dimensional
array (as contrasted with a straight-line or linear array) of
contiguous waveguides, open at one end to receive sound waves
to be absorbed and of dissimilar lengths. The ratios of the
lengths of the several waveguides conform to specified para-
meters, so as to provide a wide range of lengths within each
funcitonal group or bundle, hereinafter referred to as a
cell. Also, the flow resistance of the cell is constrained
within prescribed limits for optimum performance, this para-
meter being controlled by the geometry of the waveguides,
and, in certain cases augmented by a flow-resist~ve facing
sheet. Each waveguide is terminated with a reflective
lOS1351
termination. Each element of a sound wavefront approaching
the array finds at least one waveguide within a surrounding
area ~ (viz., "capture area") which is effectively re-
sonant at the frequency of its approaching wave. The local
resonance serves to absorb the acoustic energy at its fre-
quency throughout a capture area of about ~ . This is the
basic operating principle of all resonator arrays in the
prior art and, of course, this effect occurs in the present
invention as well.
It has now been discovered that the sound absorb-
ing efficiency and bandwidth of absorption may be substanti-
ally improved provided only that certain further geometric
constraints are adhered to which assure another additional
mechanism of sound absorption. Given one waveguide of
length Ll, and hence resonant at some frequency Fl, and a
second waveguide of length L2 = 12 Ll, resonant at frequency
F2 = 2Fl, then as the frequency is swept from Fl to F2 first
the longer waveguide of length Ll will resonate and then ~he
second waveguide of length L2 will resonate at frequencies
between Fl and F2 such that at their average resonant fre-
quency F = F12 2, both waveguides are relatively inactive.
It should be noted at this point that the responses of the
two waveguides to the intermediate frequency Fl are opposite
in phase relative to the instantaneous sound pressure. If
sound pressure strikes the two at the same instant the
associated airflow is into one waveguide and out of the
other in a "push-pull" manner. This corresponds to the
mathematical statement that Zl and Z2 are opposite in
sign.
If and only if the two waveguides are sufficiently
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105135~
close together to assure significant overlap of their cap- -
ture area do they interact with each other rather than simply
responding slightly and independently to the intermediate
sound frequency. If their capture areas overlap then the
push-pull phasing in their responses sets up a vigorous ~
local circulation (viz., near field) with an associated sub- ~ -
stantial energy absorption to the intermediate frequency
sound.
Thus, an important feature of this invention is
in part the provision of the geometry required to assure
that for virtually every given waveguide, a second waveguide
is present within a distance assuring the overlap of their
capture areas and thus assuring the substantially increased
efficiency of sound absorption.
A sound wave approaching the array finds at least ~-
one waveguide within an area = ~ which is effectively re-
sonant at the frequency of the approaching wave. The remain-
ing waveguides within the area are not resonant to that fre-
quency. The local resonance sexves to absorb the acoustic
energy at its frequency throughout a "capture area" of up to
about ~2/~. Thus, the resonant waveguide effectively serves
the entire area. While it is desirable to have the wave-
guides as close as possible to each other, practical con-
siderations dictate the actual minimum spacing between inter-
acting waveguides. As the spacing between interacting wave-
guides increases, the overall sound absorption performance
becomes progressively degraded. A practical, though some-
what arbitrary, limit for the maximum spacing between the
two interacting waveguides may be defined as no more than the
length of the longer waveguide of the pair. To attain the
~ 051351
required inner geometry the entlre pattern of the array
is repeated at frequent intervals glving a striped or
checkered appearance and is an essential distinguishing
feature between the present invention and the previously-
described prior art devices which utillze an assortment
of differently tuned resonators distributed in some ar-
bitrary manner.
- The present invention provides a sound absorbing
panel compr~sing: first and second wavegu~de arrays each
compri3ing a plurality of side-by-side acoustical wave-
gul~eg of non-uniform length and havlng adjacent ~en ends
definlng the sound-receiving end of the array, the sound- ,
receiving end of like waveguides ln each of said arrays
being spaced from each other by a distance not ~ore than .
approximately the wavelength of the sound to be absorbed .
divided by the square root of pls and wavegulde termin-
atlng means ~o disposed with re~pect to said waveguides
at the ends thereof opposite sald open ends as to result
in an àrray of waveguide6 having different lengths and
different resonant frequencies.
The pre~ent lnventlon also provldes a sound ab-
~orblng structure, comprislng: a plurality of acoustlcal
wave~uides having dlssimllar lengths such that ~n ~
(1 - n~)~0, where lo: iB equal to the length of the longest
of sald waveguides Qn is the length of the nth waveguide
and n is an index number 0, 1, 2, 3, etc~, and ~ is the
docrement of length, said waveguides havlng their sound-
recelving ends in mutual proximity; and, a plurality of
termlnatlng means, equal in number to the number of said
waveguldes, each of
., . , , . ...................... ~
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lOS~351
which acoustically terminates a corresponding one of said
waveguides at the end thereof away from the sound-receiving
end, said plurality of waveguides being disposed with respect
to each other in such a way that for any one waveguide of a
first given length other than the shortest of said waveguides
there is another waveguide approximately half as long as
said first gi~en length with its sound-receiving end disposed
s~ d
~, with respect to the sound-receiving end of ~a~ one wave-
... .
guide, at a center-to-center distance which is not greater
than said first given length.
The features and objects of the present invention
will be best under~tood from the following description of
the accompanying irawings, in which:
FIGURE 1 is a perspective view, partially broken
away, illustrating a first preferred embodiment of the in-
vention;
FIGURE 2 is a side eleYation view of a second
embodiment of the invention employing an internal supporting
structuret
FIGURE 3 is a side elevation view of a third
embodiment of the invention comprising a sound absorptive
psnel which is functionally effective on both faces;
FIGURE 4 is a modification fo the apparatus of
FIGURE 1 wherein the cells are recessed within individual
compaxtments having a common facing sheet;
FIGURE 5 is a network circuit analog of the ~ .
apparatus of FIGURE 4, and
FIGURE 6 is a network circuit analog of the ap-
paratus of FIGURE 1.
~he present invention comprises a resonant-type
1051351
absorber which offers an unu~ually wi~e absorption frequency
range. As shown in FIGURE 1, a typical embodiment comprise~
a fine honeycomb core structure 1 having proximate bundles
of waveguides, each terminated at the closed ends by an
oblique partition 2. Each operative unit is enclosed within
a group bounded by wall members 3-6 and consists of a bundle
(large in number) of parallel acoustical orifices and wave-
guides. The bundle of waveguides (1) i8 cut obliquely so
that the effective lengths of the waveguides vary along the
plane of the cut. The preferred angle of the oblique cut
will be discussed more fully hereinafter. A porous or non-
porous ~heet or partition 2 i~ located at the plane of the
cut. It is required only that the oblique element (2) be
sound reflective either by virtue of a high flow resistance,
or by being solid, or by virtue of having considerable
acoustic impedance. In a practical construction, the struc-
ture may include an impermeable backing sheet 7.
Honeycomb core, of conventional and well-known
construction, may be used in the fabrication of the wave- ;~
guide9. The core may comprise hexagonal cross-section
honeycomb, as shown in FIGURE 1, or may have various other
cross-sectional shapes such a~ round, square, triangular,
etc. In a typical construction there are a total of 100
waveguides, each 1/8 inch across, located in each group.
Since there is more than one waveguide of each length within
the group, in this particular embodiment, the group function-
ally may comprise more than one "cell" as previously defined.
In FIGURE 1 wall member 6 is shown as being broken away from
the described group in order to expose the const~uction of
the internal elements. The depth of the deepest honeycomb
',, . . '. . ' ..': ~ -,'' , - '
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~05~35~ :
core element (e.g., element 8) may, for example, be one
inch. A complete cycle of depth (viz., the intergroup
spacing) should be located within a similar distance. Be-
cause of the "sawtooth" topography of the end-closing parti-
tion of the groups, if planned for use as a duct lining,the device may have a preferred orientation relative to the
direction of the impinging sound and air flow. Also, the
device optionally may be provided with a sound permeable
facing sheet 9 for ~tructural, esthetic or other purposes.
The core or honeycomb structure 1 making up the
bundle of waveguides may be fabricated from plastic, paper,
metal, ceramic, or other suitable material as dictated
principally by the intended environment or operation and/or
economic constraints. Similarly, the group enclosing walls
(e.g., 3-6) and the backing sheet 7 may be made of either
metal or non-metallic materials as may be appropriate. The
entire structure may be assembled by welding, adhesive bond-
ing mechanical interlocking arrangement, or other suitable
means. It is the geometry and configuration of the elements
that principally determine the operating parameters, rather
than the intrinsic properties of the materials from which
the device is constructed. Hence, the designer has a wide
range of design alternatives with respect to selection of
materials for fabrication.
A sound wave approaching the array of differently
tuned waveguides (l) will encounter at least one that is
resonant, or nearly so, at the frequency (viz., admittance
is large). The remaining waveguides within the cell (3-6)
are not resonant to that frequency (viz., admittance is
small). The local resonance absorbs some of the acoustic
lOSi35~
energy at its frequency through an area as large as about
~2/~. For this reason the cell pattern is repeated so as to
cover contiguous A2/~ areas. At the lower frequencies a
particular waveguide may be resonant for the entire cell by
reason of the fact that the cell is dimensioned to be within
the aforementioned spacing constraint. Above a frequency
roughly double the lowest resonant frequency the capture
area ,~ becomes less than the cell area and the resonance
mechanism becomes progressively less effective. For the
geometry shown in FIGURE 1-4 the length of any two waveguides
differ so abruptly that the overlap of thei~ capture areas
is apparent within the confines of the cell. The response
of any such cell pair to any frequency intermediate between -;
their resonant frequency is of the nature of a push-pull
because the shorter one is operating below resonance (Z~ 0) ;
and the longer one is above resonance (z C0).
The resulting vigorous near field leads to vis-
cous losses which provide the dissipation of energy needed
to attenuate the sound. In thi9 way and by this mechanism
the sound absorption remains làrge even at very high fre-
quencies for which the actual capture areas have become very
small.
The intense near field sonic activity occurring
within the waveguides provides the necessary damping for
efficient sound absorption even though the terminating plate
~partition 2) is not designed to be permeable. Damping due
to scrubbing on the walls of small tubes (l) is proportional
to frequency, which helps to explain the increasing acoustic
resistance that has actually been observed in practical
constructions. ~`
.
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1051351
The oblique element terminating the waveguides
(viz., partition 2) should, as has previously been mentioned,
be substantially reflective; hence, the reason for a solid
partition in a preferred construction. However, this ele-
ment may derive its reflectance by virtue of a high flowresistance, or by having considerable acoustic inertance.
For example, an oblique termination operating as a high-
inertance mechanism may comprise a foraminous plate having
a small percentage of open area. This would yield the re-
quired reflectance, but would desirably provide liquiddrainage to each waveguide as may be required in certain
types of installations.
In the embodiment of FIGURE 1, the group enclosure
comprising wall members 3-6 is shown to have a square cross
section. This shape is arbitrary. If desired, the boundar-
ies of a cell or group of cells may, as in the case of the
waveguides, have any desired cross-sectional shape such as
hexagonal, round, triangular, rectangular, etc. The princi-
pal operating parameter with respect to the configuration of
the cell is that it have a maximum over-lapping of capture
areas between as many waveguide pairs as possible. Also,
the construction shown in FIGURE 1 employs an ob}ique planar
partition 2 for terminating the plurality of waveguides
within the corresponding cell. As will be appreciated,
partition 2 need not be planar since other surface configura-
tions such as conical, exponential, etc., could be utilized
and still yield the necessary differences in depth of the
several nearby waveguides. The essential consideration is
that the bundle of waveguides be terminated in s~ch a manner
that the depths of the several waveguides vary through a
11
~ 05135~
range of dimensions sufficiently wide to accommodate the
sound spectrum of interest.
In order to obtain the desired area overlap or
"capture effect" of the close1y-spaced waveguides, it is
necessary to have at least one waveguide within each cell
which is below resonance and one above resonance at the fre-
quency of the incoming wave. To assure this, the ratio of
length of the longest waveguide to that of the shortest wave-
guide should be as high as possible. That is, the rate of
change of waveguide length (the slope of oblique partition
2) is an important parameter. Sufficient slope improves ;
performance and permits the use of coarser, larger cell
sizes. Since each waveguide has an effective sound-receiving
area that is greater than its actual cross-sectional area, -~
the waveguides comprising each cell should be so tightly
packed that the "effective" area of any waveguide at reson- -~
ance always overlaps the effective areas of any other wave-
guide at antiresonance. This is accomplished by varying
the lengths of the waveguides within the cell abruptly. This
is assured if the angle of elevation of the partition 2 is
at least 45. Below 45, the resonators take increasingly
independent operating (viz., non-parallel) characteristics,
and performance deteriorates. For angles greater than 45,
little further improvement occurs at the lower frequencies,
but some further improvement occurs at very high frequencies.
The invention operates because the differing
waveguides are not only tuned to different resonant fre-
quencies, but also because they act with predetermined phase
relationships. Specifically, they are spaced closely enough
to permit phased interaction rather than independent
iO5135~
operation.
Any resonator undergoes a rapid phase shift of
the oscillating flow relative to the pressure wave as the
frequency passes from below resonance to above resonance.
If the damping is relatively light, this phase shift amounts
to nearly 180 degrees. Thus, given two widely spaced apart
resonant tubes, one of which is twice the length of the
other, at any given frequency between the two first resonant
frequencies the flow will be entering the first tube and
will be leaving the second tube at a particular instant in
time. I e the two tubes are placed close enough together,
their effective areas will overlap. To assure this, the
center-to-center distance between the tubes must be reduced
to approximately one-quarter wavelength of the resonant fre-
quency of the shorter tube. Since one tube is only half thelength of the other, the angle between the common entrance
plane of the pair of tubes and that of the closed ends of
the tubes is about 45. If this angle is much less than 45
the geometry requires that they be more widely spaced apart
and the consequence is that they will act independently.
If, on the other hand, the effective areas of the -
two resonators overlap, a vigorous interaction occurs and
they no longer act independently, but rather are said to act
in parallel coupling. At frequency Fl, the first tube is
resonant and the second tube quiescent, and conversely. At
frequency F = F12+ F2 a resonant-like condition exists in-
volving a strong local circulation between the two tubes.
This is called a "near field." This vigorous near field
local circulation into and out of both tubes results in much
greater acoustical energy absorption than the combined effect
13
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~OS1351
of the resonators acting independently at frequency F because
neither is resonant by itself at F.
To assure the desired parallel coupling with
practically realizable geometries, while maintaining the
necessary small inter-cell spacing, requires that the ratio
of the depths of the shortest waveguide to the longest wave-
guide in any given cell be quite large (i.e., equal to or
greater than 1:2). This corresponds to a large diagonal
slope (i.e., ~30) of the plane through the closed ends of
the waveguides).
Other structural modifications may be made to
provide load-bearing properties or other characteristics
dictated by the intended operating environment. For example,
there is shown in FIGURE 2 a cross-sectional elevation view
of a resonant type sound absorber panel constructed in
accordance with the invention, having potentially greater
structural strength than the configuration of FIGURE 1.
This embodiment c~mprises a non-porous backing sheet 11 and
a substantially sound transparent facing sheet 12. Cell
enclosing walls 13 and 14 are perpendicularly disposed be-
tween mutually confronting backing sheet 11 and spaced apart
facing sheet 12. The bundle of waveguides within each cell
is fabricated from an integral honeycomb core element. In
the course of manufacture of the panel, the honeycomb core
element for each cell is first cut on a bias so as to divide
the element into an upper and lower section 15 and 16, re-
spectively. The reflective terminating partition 17 is then
interposed between the upper a~d lower sections 15 and 16. i
The operative, sound absorbing, section lS is exposed to
the incoming sound wave through sound-transparent facing
14
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1051351
she~t 12. The lower section 16 serves primarily to support
the partition 17 and lend structural rigidity to the overall
device. Also, this construction minimizes the requirements
for attaching or otherwise securing the partition and the
waveguide members to the adjoining cell-defining members.
Again, it is not necessary that the partition 17 be a planar
oblique element since it could have a curved, angular, or
other compound shape, as desired, to vary the effective depth
of the tubular sound-receiving portions of the honeycomb ele-
ment 15.
There is shown in FIGURE 3 yet another embodimentof the invention which is characterized by having two sound
absorbincJ faces. This embodiment is generally similar to
that of FIGURE 2 and comprises group-defining wall members
18 and 19, and upper and lower honeycomb core sections 21
and 22, respectively. The core sections 21 and 22 are
separated by an interposed sound reflective partition 23.
Unlike the construction of FIGURE 2 (which has a non-porous
backing sheet 11), the embodiment of FIGURE 3 is provided
with separate sound transparent sheets on both sides of the
panel. That is, the waveguide bundle comprising upper sec-
tion 21 is covered by sound transparent sheet 24, and the
waveguide bundle comprising lower section 22 i9 covered by
sound transparent sheet 25. Since the panel structure i8
symmetrical about its central axis 26, sound approaching
either side of the panel will be absorbed. As in the case
of the previously described embodiments, the topography of
the partition that reflectively terminates the waveguide may
be either planar or curved as desired.
There is shown in FIGtlRE 4 an alternative
10513Sl
embodiment of the invention. This construction comprises a
plurality of cell groups each enclosed on four sides. Typi-
cal wall members enclosing the sides of the cell groups are
indicated at 32 and 33. It should be understood that the
two remaining wall members (not shown in FIGURE 4) for the
cells bounded by members 32 and 33 are orthogonally disposed
thereto in order to form a four-sided cell group having a
square cross sectlon. This square shape is arbitrary and i8
by way of example only. A bundle of waveguides 31 is located
within the cell group. The open, sound-receiving, ends of
the waveguides (31) are at the top of the cell group, as
viewed in FIGURE 4. A solid wall member 34 closes the bottom
ends of the cell groups. An oblique planar partition, such
as that indicated at 35, terminates the plurality of wave-
guides within each cell. A permeable facing sheet 36 ex-
tends across the open ends of all of the cell groups.
As can be seen, the depth of the cell groups is
greater than the depth of the longest waveguide disposed
therein, thereby providing an open area or cavity 37 between
- 20 the sound receiving ends of the waveguides and the permeable
facing sheet 36. That is, the bundle of waveguides 31 is
recessed within the cell cavity 90 as to be spaced apart
from the facing sheet 36. Functionally, the facing sheet 36
i5 common to all of the cells comprising the array, and
operates as a series acoustical resistance for the entire
array. This arrangement provides a slightly different ab- -
sorption spectrum shape than would be obtained without the
cavity 37. The configuraiton shown in FIGURE 4 is preferred
where it is desired that a coarse perforate be used having
holes comparable to the diameter of the waveguide entrances.
16
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10~1351
To facilitate a comparison between these two embodiments of
the invention there is shown in FIGURES 5 and 6 electrical
network analogs which correspond to the acoustical apparatus
of FIGURE 4 and FIGURE 1, respectively.
Referring first to FIGURES 4 and 5 there is shown
the electrical network equivalent of the apparatus of FIGURE
4 wherein terminal 3a comprises the input to the device, and
serie~ resistance 39 corresponds to the acou~tical resistance
of the facing member 36. The capacitive reactance, and the
wall-scrubbing resistance of each cell in the array (as pro-
vided by the then-active waveguide within each cell) is
represented by a series capacitance and resistance. For
example, the active waveguide in the first cell corresponds
to capacitance 41 and resistance 45, the next cell corre-
sponds to capacitance 42 and resistance 46, and 80 forth
throughout the parallel array comprising branch capacitances
41-44 and series resistances 45-48. The network is refer-
enced to ground terminal 49.
As can be seen, resistance 39 (and hence the flow
resistance of facing sheet 36) is in series with the parallel
combination of all of the capacitances 41-44 and resistances
45-48 (which correspond to the overall array).
The network of FIGURE 6 corresponds to the appara-
tus of FIGURE 1 and is provided with an input terminal 51.
Resistances 52-55 correspond to the resistances of the in-
dividual areas of the facing sheet 9 which extend over the
open area of each individual waveguide within a cell. Capac-
itances 56-59 correspond to the acoustical capacitive reac-
tances of corresponding waveguides, and resistances 61-64
correspond to the scrubbing resistances of corresponding
~OS1351
waveguides. The network is referenced to ground 65.
Certain precautions must be taken with respect to
obtaining valid result~ from the foregoing network analogs.
The parallel waveguide~ can be represented by their parallel
circult elements only if the waveguides are packed so closely
that they act in parallel ~i.e., if their capture areas
overlap such that they act in parallel rather than indepen-
dently). Acoustic resistance~ and reactances must be ex-
pressed in units of acoustical ohms to be analogous to elec-
trical ohms.
The acousitc reactance of the waYeguide is in
reality of the form: X = -; cot c~ L and is approximated by
a capacitance only at low frequencies.
In summary, the present invention, in all embodi-
ments, comprises a parallel-coupled system because of the
close constraint of the inter-cell spacing and because of
the wide range of depths of the waveguides, whereby the
effective areas of the waveguides at resonance always over- ~-
lap with the area~ of other waveguides at anti-resonance.
Other modifications may be made in order to
~ccommodate particular applications. For example, the over-
all structure may have a curved shaped (as contrasted with
planar facing or bàcking sheets) as may be required for
lining a circular duct or other curved boundary. Also, the
facing sheets may be omitted without impairing the sound
ab~orptive properties of the device. Still other modifica-
tions may be made by tho~e versed in the art without depart-
ing from the invention-as set forth above.
18
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