Loudspeaker Cabinet Bracing Analysis using
Analytical and Experimental Methods
Andy J. LaCombe
Test Products Application Manager
SDRC, Integrated Test Products
2000 Eastman Drive
Milford, OH 45150 USA
ABSTRACT
1. INTRODUCTION
The goal of this project was to determine the
optimum bracing configuration for a standard
loudspeaker box. Typically, braces are placed
where experience has shown them to be “best”
located, and at locations that the designer “thinks”
will solve a vibration problem. Some people have
been quoted as saying that such and such a
configuration “eliminated” cabinet vibration. This
is a” acceptable method, but using finite element
modeling in conjunction with experimental modal
analysis and boundary element analysis will help
prevent potential cabinet vibration problems from
arising later in the product life cycle. There has
been little verification work published as to the
validity of typical bracing configurations.
Historically, the loudspeaker industry has not
published information on bracing of loudspeaker
cabinets. This does not mea” that the work has
not been done, but that there has not been a great
deal of discussion about methods or styles of
cabinet bracing backed up by analytical methods.
This paper will discuss the initial modeling of a
standard loudspeaker box using a Finite Element
Model (FEM) as the starting point, and
Experimental Modal Analysis (EMA) to verify the
FEM. A Boundary Element Model (BEM) was also
used to ensure that the bracing configurations did
not adversely affect the acoustical pressure inside
the cabinet. The work done for this project was not
exhaustive and will require follow-up work to
complete the analysis at a later time. A list of
additional topics to be covered appears at the end
of this paper.
A” FE Model of the bare cabinet was constructed
and verified using experimental modal analysis.
Then a boundary element analysis was used to map
out the initial pressure distribution inside the
cabinet so that the initial bracing scheme could be
planned. Iterations on bracing configurations were
performed based on the vibration signature of the
cabinet and the internal pressure distribution. A
boundary element analysis was performed for
several configurations to ensure that a bracing
configuration did not cause a pressure build-up
behind the woofer.
The goal was to show how these types of modeling
and verification tools can be used to guide the
design of a loudspeaker cabinet.
It was also
intended to show bracing schemes that provide
maxi”““” vibration control with the least amount
of construction cost and effort.
2.
f=
BACKGROUND
There are many areas of concern for the speaker
designer. The inherent cabinet vibration is not
usually high on the list of priorities, except in
esoteric designs. The designer is more concerned
with the internal volume of the box, the electrical
cross-over network, the drive unite., and most of
all, cost.
GLOSSARY OF SYMBOLS
“X
Lx,
c
A=
I=
HISTORICAL
al Svmbols
Integers 0, 1, 2, . ..) Dimensions of enclosure
Speed of sound
Wavelength
Path length
Frequency
The quality of the design is judged by the types of
measurements made on the completed speaker.
Subtle problems in the design can be detected by
listening to the speaker and verified by
measurements, but not all measurements are
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capable of detecting all problems. A standard three
meter response measurement may not detect
problems associated with cabinet vibrations, where
acceleration measurements on the cabinet would.
In many instances, the designer needs to know
what problems to looks for so that the proper types
of tests can be made to detect these them.
modes were within ten percent.
At this point
modifications were made to the FE Model to test
out different bracing schemes.
One area that was not modeled in sufficient detail
was the boundary between the six panels that
make up the box. They were modeled as solid
connections, which explains partially why the FE
modes were higher in frequency that the test
modes.
The ideas presented in this paper are meant to
suggest alternative methods for cabinet design.
They will provide a better first prototype by
disqualifying some variations before they are
produced. This will save time during the design
cycle and prevent major reworking of the design
after the first prototype.
Table 1 shows the results of the various brace
configurations.
Cabinet
Description
Standard Box, no braces
Vertical Brace front to back
Horizontal Brace Middle
Horiz & Vert Braces
3 Horiz & 1 Veti Braces
3H, 1V & Corner Beams
3. FINITE ELEMENT ANALYSIS
The first decision to be made for the dynamic
analysis of the cabinet was to determine what type
Solid
of elements to use for the model.
Tetrahedrons were not even considered because
they are too stiff for dynamic analyses. The main
comparison came down to Bricks versus Shells. A
test run using each of these element types was
made to determine how much the results would
vary with each type. The results of the dynamic
analysis were within 1% so the remainder of the
modeling was done with shells, for ease of meshing
and solution speed.
Mods
296
424
527
642
1016
866
1
Mode
a
422
446
550
658
1019
1038
Table 1: Cabinet configurations
The configuration descriptions are as follows:
o #l -The standard box was the bare box with
no internal bracing.
o #2 - The first variation added a vertical
brace that ran from the front of the box the’
back, and top to bottom.
The next thing to decide was how much detail
concerning the hole for the woofer would be
included. A model was run with the hole in place
and one without the hole. The results showed that
the first few flexible modes for the model with the
hole were within three percent of the model
without the hole. The model without the hole was
chosen to complete the analysis. This also helped
to reduce the complexity of the model and the
solution time.
o #3 The horizontal brace was positioned in
the middle of the cabinet and connected the
for vertical panels.
o
#4 Configurations two and three were
combined.
o #5 - Two additional horizontal panels were
All three
added to configuration four.
panels were equally spaced from the top to
bottom of the cabinet.
Material properties for plywood are not easy to
come by, and those that were found did not match
There are several
the prototype box material.
variations in the way that plywood is made. The
first is the number of plys. Plywood is made up of
an odd number of plys, and most often made up
from 5 plys. These plys can all be made from pine,
or ply numbers 2 and 4 can be made from a
material that is similar to particle board. The
relative merits of each type were not investigated,
but would make for an interesting project to
the
damping
and
stiffness
determine
characteristics of each.
o #6 The last configuration added stiffening
beams at each corner of the cabinet, that
ran from the top to the bottom.
The standard box type structure without bracing,
will exhibit panel modes of vibration as the first
flexible modes. Once the mass of the structure is
increased and the panel modes removed by the use
of bracing, the entire structure will act as a
section.
A small sample piece of plywood was used to
calculate the material density and to correlate with
an FE Model. The material properties of the small
piece were adjusted to obtain the proper first
flexible mode. Then these properties were used on
the full box. The results for the first two flexible
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Figures 1 and 2 show the first flexible modes for
the standard cabinet without bracing.
Figure 3: Configuration ~75, mode #l
The second flexible mode for this configuration
shows a torsional mode for the entire structure,
and is shown in Figure 4.
Figure 1: Standard Cabinet, mode #l
The first flexible mode is an oil can mode for all the
vertical panels, with the majority of the motion
occurring in the front and rear panels. The front
and back panels are out of phase with the two side
pMl&.
Figure 4: Configuration #5, mode #2
The last configuration added vertical beam
stiffeners to the corners of the cabinet. This setup
reduced the first flexible mode frequency because it
added to much mass for the stiffness achieved.
The mode occurs at 866 Hertz and is shown in
Figure 5. This torsional mode was the second
flexible mode in the previous configuration.
Figure 2: Standard Cabinet, mode #2
The second flexible mode is very similar to the first
except that the all the panels are phased such that
they all move inward at the same time.
Configuration number five with three horizontal
braces and one vertical brace, began to exhibit this
“section” type of vibration. Figure 3 shows the
deformation pattern for the first flexible mode at
1016 Hertz. This was the most successful bracing
scheme. This mode is a lateral bending mode of
the entire structure.
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dimensions were calculated to achieve an aesthetic
appearance.
Many speakers have dimensions
related by, 51312. The main thing to stay away
from is dimensions that are multiples of one
another (i.e., 2 x 4 x 61, to help reduce standing
wave reinforcement. Standing waves can not be
prevented, but the designer needs to be sure that
one standing wave does not reinforce another.
This situation will cause a greater problem then
two standing waves of the same amplitude, but at
non- multiple frequencies. .Standing
wave$ will be
discussed in the next section.
The cabinet was suspended on foam and impacted
at three reference locations, for the EMA. Triaxial
acceleration response measurements were made at
42 locations equally spaced on all six sides of the
Figure 5: Configuration A%, mode #I
e”ClOSUre.
The second flexible mode in this configuration is
more of a panel mode than its counterpart in the
previous configuration. This mode occurs at 1038
Hertz and is shown in Figure 6.
5. STANDING WAVES
A problem in the cabinet design is standing waves.
A standing wave occurs in an enclosure when the
radiated sound is in phase with the reflected
sound. This happens when the wavelength or any
integer multiple is equal to the path length. The
path length is any dimension of the enclosure.
Standing waves are commonly referred to as normal
modes of vibration of an enclosure. Equation (1)
shows the relationship between the wavelength
and the path length.
d=I
(1)
The frequency is equal to the speed of sound
divided by the wavelength.
f=S
(2)
Figure 6: Configuration #6, mode #2
Combining equations (1) and (2) the frequency can
be expressed as the normal mode of vibration.
A discussion of the specific cabinet and brace
models used is presented in section 7.
f/F
(3)
For the case of sound reflecting back and forth
between two surfaces separated by a distance l,.
The distance that the sound will repeat is 2 1,. The
frequency associated with this resonance is given
by equation (4).
4. EXPERIMENTAL MODAL ANALYSIS
An Experimental Modal Analysis was performed on
a prototype speaker to compare to the Finite
Element Model. The cabinet was made of 314”
plywood. The corners were rabbeted to a depth or
3/ 8”. Corner and edge cleats were used for ease of
construction, cabinet sealing and strength. With
more gluing area at the edges there is a better
chance to provide and air-tight seal.
f” =z
(4)
This equation can be extended to take into account
the three dimensions of a rectangular room. The
three-dimensional equation for normal modes of an
enclosure is shown in equation (5).
The prototype cabinet was 25.5” H x 15” W x 13.5”
D.
The internal volume of the cabinet was
determined based on the woofer chosen for this
design. The woofer selected for this design was
also best suited for a vented enclosure. Once the
internal volume was determined, individual
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It is often believed that standing haves will not
exist in an enclosure that does not have parallel
walls. This is not true, because standing waves
can set up at oblique angles to the enclosure
surfaces. Adding internal bracing will provide a
diffraction surface and cut down on the
unobstructed internal path lengths. Both of these
results will help to reduce the amount of internal
cabinet pressure. The shorter path lengths will be
associated with higher frequency standing waves.
0.138141
0.104281
6. BOUNDARY ELEMENT ANALYSIS
The boundary element software used allows for the
analysis of vibro-acoustic behavior of complex,
three-dimensional structures coupled to one or
more fluids, and subjected to mechanical or
acoustic excitations.
It is based on a general
variational formulation coupling the BEM for the
fluid to the classical FEM for a structure. The BEM
models only the boundary surfaces of a fluid and
does not need to break down the volume into
discreet elements.
Results can be calculated
inside the fluid domain by specifying “Domain
Points,” that give the BE solver a surface to
calculate acoustic or structural vibrations (i.e.,
pressure, intensity, velocity or acceleration).
0.036562
0.002703
Figure 7:
Pressure Distribution
Further work could be done to determine the
radiation pattern of the speaker.
The acoustic
sources would be the actual drive units and the
structure vibrations caused by internal cabinet
pXSSUF%
7. CABINET & BRACE DESCRIPTIONS
For the current analysis, a study of the uncoupled
cavity pressure distribution was made. The goal of
this part of the work was to determine the points of
peak pressure on the cabinet side walls. These
locations would be candidates for the location of
bracing. A check was also made to make sure that
the addition of internal bracing did not create
internal pressure peaks near the rear of the
woofer.
This analysis was performed on a basic rectangular
box to ensure that the design was simple enough
to prove the ideas presented without getting lost in
a specialized configuration. The basic box is shown
in Figure 8.
This configuration allows most
engineers and designers to feel comfortable with
the conclusions, because the results make
physical sen.se for this simple case. The author
would like to follow up this paper with another
dealing with a more advanced cabinet type,
something like a transmission-line (Acoustic
Labyrinth).
Figure 7 shows a plot of the pressure distribution
inside the cabinet. The software allows for the
calculation of the pressure distribution at discreet
frequencies.
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The second brace style is the same as the first,
except that an oval shaped hole has been placed in
its center. This brace is shown in Figure 11.
The brace with the hole did not change the first
flexible mode by more than one percent. This
showed promise for a shape optimization to cut
down on the weight of the brace while not
degrading its performance.
Figure 8: Cabinet #l, without holes
A second cabinet configuration was used with the
cutout for the woofer to determine if the results
were changed significantly due to the presence of
the hole (i.e., > 5%). This also solved the problem
of modeling the baffle with the woofer mounted in
place. This is a topic for further investigation. The
second box design is shown in Figure 9.
Figure 11: Brace #2
8. ADDITONAL WORK
The author would like to extend the work present
here by performing the following analyses:
. Perform more In-Depth BE Analysis
The current BE software used in this analysis
can determine the coupled vibro-acoustic
problem. This would require the existence of
a detailed prototype speaker, because the
drive units performance would be required.
The drive unit performance spectra would be
used as inputs to the vibro-acoustic model
and the resultant cabinet radiation could be
determined.
Figure 9: Cabinet #2, with woofer cutout
Two different braces were used inside the designs
shown above. The first one is a simple rectangular
section, shown in Figure 10.
This type of study can help assess the
contribution of the cabinet to the overall
sound field produced by the speaker. When
the cabinet modes are higher in frequency,
they will have less energy to cause cabinet
radiation problems.
* Optimize Hole in Center Brace
This would involve using shape optimization
to determine the optimum shape of the hole
in the brace, while maintaining the frequency
of the first flexible mode of the cabinet.
- Optimize Brace Thickness
l Optimize Front Baffle Thickness
Figure 10: Brace #l
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l
Optimize AZZ Panels (Thickness)
All three of these optimizations involve the
use of a thickness optimization package to
determine the optimum thickness of all
It will take a bit of effort to
panels.
determine which panels to optimize together
and which to optimize separately.
It is
advisable to not change the material for the
outside of the box to a non-standard size, to
keep costs down. It is also better to change
one panel that would provide the most benefit
instead of several panels to achieve the same
effect, again to reduce costs.
The analysis of a more complex structure
would help to prove the ideas presented in
this paper. The first step would be to do the
final analysis using the full detail of the
cabinet (driver, vent and connection holes).
Then a more complex speaker type can be
analyzed to determine if these methods can
help non-standard geometries (like the
transmission line).
9. SUMMARY
This work was meant to provide readers with some
background information on the problems with
loudspeaker cabinet vibrations, and some tools to
help design bracing schemes. These braces will
either reduce the vibration to an acceptable level,
or move the frequency to a location more desirable.
Problem modes are usually moved higher in
frequency so that they will not be in the low
frequency operating range of the woofer.
There is a point where too much bracing will
increase the total mass of the structure and result
in section modes of vibration rather than local
panel modes. In this analysis the first flexible
mode changed to a whole cabinet lateral bending
mode rather than a side-panel “oil-can” mode. This
result along with no further improvement in first
mode frequency showed the optimum configuration.
Weight is something that is important to address
to keep down construction and shipping costs. An
optimization analysis can determine the optimum
brace thickness. Many of these ideas presented
will depend on the market the design is going after.
Exotic bracing schemes will drive the final cast of
the speaker up due to development, construction
and shipping.
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