Note: Descriptions are shown in the official language in which they were submitted.
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WO 99/52322 PC'T/GB99/01048
1
TITLE: ACOUSTIC DEVICE
DESCRIPTION
TECHNICAL FIELD
The invention relates to acoustic devices and more
particularly, but not exclusively, to loudspeakers
incorporating resonant mufti-mode panel acoustic radiators,
e.g. of the kind described in our International application
W097/09842. Loudspeakers as described in W097/09842 have
become known as distributed mode (DM) loudspeakers.
Distributed mode loudspeakers (DML) are generally
associated with thin, light and flat panels that radiate
acoustic energy equally from both sides and in a complex
diffuse fashion. While this is a useful attribute of a DML
there are various real-world situations in which by virtue
of the applications and their boundary requirements a
monopolar form of a DML would be preferred.
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In such applications the product may with advantage be
light, thin and unobtrusive.
BACKGROUND ART
It is known from International patent
application W097/09842 to mount a multi-mode resonant
acoustic radiator in a relatively shallow sealed box
whereby acoustic radiation from one face of the radiator
is contained. In this connection it should be noted that
the term 'shallow' in this context is relative to the
typical proportions of a pistonic cone type loudspeaker
drive unit in a volume efficient enclosure. A typical
volume to pistonic diaphragm area ratio may be 80:1,
expressed in ml to cm2. A shallow enclosure for a resonant
panel loudspeaker where pistonic drive of a lumped air
volume is of little relevance, may have a ratio of 20:1.
DISCLOSURE OF INVENTION
According to the invention an acoustic device
comprises a resonant multi-mode acoustic resonator or
radiator panel having opposed faces, means defining a
cavity enclosing at least a portion of one panel face and
arranged to contain acoustic radiation from the said
portion of the panel face, wherein the cavity is such as to
modify the modal behaviour of the panel. The cavity may be
sealed. A vibration exciter may be arranged to apply
bending wave vibration to the resonant panel to produce an
acoustic output, so that the device functions as a
loudspeaker.
The cavity size may be such as to modify the modal
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3
behaviour of the panel.
The cavity may be shallow. The cavity may be
sufficiently shallow that the distance between the internal
cavity face adjacent to the said one panel face and the one
panel face is sufficiently small as to cause fluid coupling
to the panel. The resonant modes in the cavity can
comprise cross modes parallel to the panel, i.e. which
modulate along the panel, and perpendicular modes at right
angles to the panel. Preferably the cavity is sufficiently
shallow that the cross modes (X,Y) are more significant in
modifying the modal behaviour of the panel than the
perpendicular modes (Z). In embodiments, the frequencies
of the perpendicular modes can lie outside the frequency
range of interest.
The ratio of the cavity volume to panel area (ml:cm2)
may be less than 10:1, say in the range about 10:1 to 0.2:1.
The panel may be terminated at its edges by a
generally conventional resilient surround. The surround
may resemble the roll surround of a conventional pistonic
drive unit and may comprise one or more corrugations. The
resilient surround may comprise foam rubber strips.
Alternatively the edges of the panel may be clamped in
the enclosure, e.g. as described in our co-pending PCT
patent application PCT/GB99/00848 dated 30 March 1999.
Such an enclosure may be considered as a shallow tray
containing a fluid whose surface may be considered to have
wave-like behaviour and whose specific properties depend on
both the fluid (air) and the dimensional or volume box
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4 '
geometry. The panel is placed in coupled contact with this active
wave surface and the surface wave excitation of the panel excites the
fluid. Conversely the natural wave properties of the fluid interact
with the panel, so modifying its behaviour. This is a complex coupled
system with new acoustic properties in the field.
Subtle variations in the modal behaviour of the panel may be
achieved by providing baffling, e.g. a simple baffle, in the enclosure
and/or by providing frequency selective absorption in the enclosure.
Fr~n another aspect the invention is a method of modifying the
modal behaviour of a resonant panel loudspeaker or resonator,
comprising bringing the resonant panel into close proximity with a
boundary surface to define a resonant cavity therebetween.
BRIEF DESCRIPTION OF DRAWINGS
Figure 1 is a cross section of a first embodiment of sealed box
1 5 resonant panel loudspeaker;
Figure 2 is a cross-sectional detail, to an enlarges scale, of
the e~r~bodiment of Figure 1;
Figure 3 is a cross section of a second embodiment of sealed box
resonant panel loudspeaker;
2 0 Figure 4 shows the polar response of a DNIL free-radiating on
both sides;
Figure 5 shows a ccc~arison between the sound pressure level in
Free Space (solid line) and with the ~ arranged 35mm frarn the wall
(dotted line)
2 5 Figure 6 shows a comparison between the acoustic power of a DNIL
in free space (dotted line) and with a baffle around the panel between
the front and rear;
Figure 7 shows a loudspeaker according to the invention;
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Figure 8 shows a DML panel system;
Figure 9 illustrates the coupling of components;
Figure 10 illustrates a single plate eigen-function;
Figure 11 shows the magnitudes of the frequency
5 response of the first ten in-vacuum panel modes;
Figure 12 shows the magnitudes of the frequency
response of the same modes in a loudspeaker according to
the embodiment of the invention;
Figure 13 shows the effect of the enclosure on the
panel velocity spectrum;
Figure 14 illustrates two mode shapes;
Figure 15 shows the frequency response of the
reactance;
Figure 16 illustrates panel velocity measurement;
Figure 17 illustrates the microphone set up for the
measurements;
Figure 18 shows the mechanical impedance for various
panels;
Figure 19 shows the power response of various panels;
Figure 20 shows the polar response of various panels;
Figure 21 shows a microphone set up for measuring the
internal pressure in the enclosure;
Figure 22 shows the internal pressure contour;
Figure 23 shows the internal pressure measured using
the array of Figure 21;
Figure 24 shows the velocity and displacement of
various panels;
Figure 25 shows the velocity spectrum of an A5 panel
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in free space and enclosed;
Figure 26 shows the velocity spectrum of another A5
panel in free space and enclosed;
Figure 27 shows the power response of an A2 panel in
an enclosure of two depths, and
Figure 28 illustrates equalisation using filters.
In the drawings and referring more particularly to
Figures 1 and 2, a sealed box loudspeaker 1 comprises a
box-like enclosure 2 closed at its front by a resonant
panel-form acoustic radiator 5 of the kind described in
W097/09842 to define a cavity 13. The radiator 5 is
energised by.a vibration exciter 4 and is sealed to the
enclosure round its periphery by a resilient suspension 6.
The suspension 6 comprises opposed resilient strips 7, e.g.
of foam rubber mounted in respective L-section frame
members 9,10 which are held together by fasteners 11 to
form a frame 8. The interior face 14 of the back wall 3 of
the enclosure 2 is formed with stiffening ribs 12 to
minimise vibration of the back wall. The enclosure may be a
plastics moulding or a casting incorporating the stiffening
ribs.
The panel in this embodiment may be of A2 size and the
depth of the cavity 13 may be 90mm.
The loudspeaker embodiment of Figure 3 is generally
similar to that of Figures 1 and 2, but here the radiator
panel 5 is mounted on a single resilient strip suspension
6, e.g. of foam rubber, interposed between the edge of the
radiator 5 and the enclosure to seal the cavity. The
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radiator panel size may be A5 and the cavity depth around 3
or 4 mm.
It will be appreciated that although the embodiments
of Figures 1 to 3 relate to loudspeakers, it would equally
be possible to produce an acoustic resonator for modifying
the acoustic behaviour of a space, e.g. a meeting room or
auditorium, using devices of the general kind of Figures 1
to 3, but which omit the vibration exciter 4.
It is shown that a panel in this form of deployment
can provide a very useful bandwidth with quite a small
enclosure volume with respect to the diaphragm size, as
compared with piston speakers. The mechanisms responsible
for the minimal interaction of this boundary with the
distributed mode action are examined and it is further
shown that in general a simple passive equalisation network
may be all that is required to produce a flat power
response. It is also demonstrated that in such a
manifestation, a DML can produce a near-ideal hemispherical
directivity pattern over its working frequency range into a
2Pi space.
A closed form solution is presented which is the
result of solving the bending wave equations for the
coupled system of the panel and enclosure combination. The
system acoustic impedance function is derived and is in
turn used to calculate the effect of the coupled enclosure
on the eigen-frequencies, and predicting the relevant
shifts and additions to the plate modes.
Finally, experimental measurement data of a number
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samples of varying lump parameters and sizes are
investigated and the measurements compared with the results
from the analytical model.
Figure 4 illustrates a typical polar response of a
free DML. Note that the reduction of pressure in the plane
of the panel is due to the cancellation effect of acoustic
radiation at or near the edges. When a free DML is brought
near a boundary, in particular parallel with the boundary
surface, acoustic interference starts to take place as the
distance to the surface is reduced below about l5cm, for a
panel of approximately 500 cm2 surface area. The effect
varies in its severity and nature with the distance to the
boundary as well as the panel size. The result, nonetheless
is invariably a reduction of low frequency extension,
peaking of response in the lower midrange region, and some
aberration in the midrange and lower treble registers as
shown in the example of Figure 5. Because of this, and
despite the fact that the peak can easily be compensated
for, application of a 'free' DML near a boundary becomes
rather restrictive. '
When a DML is placed in a closed box or so-called
"infinite baffle" of sufficiently large volume, radiation
due to the rear of the panel is contained and that of the
front is generally augmented in its mid and low frequency
response, benefiting from two aspects. First is due to the
absence of interference effect, caused by the front and
rear radiation, at frequencies whose acoustic wavelengths
in air are comparable to the free panel dimensions; and
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second, from the mid to low frequency boundary
reinforcement due to baffling and radiation into 2Pi space,
see Figure 6. Here we can see that almost 20 dB
augmentation at 100Hz is achieved from a panel of 0.25 mz
surface area.
Whilst this is a definite advantage in maximising
bandwidth, it may not be possible to incorporate in
practice unless the application would lend itself to such a
solution. Suitable applications include ceiling tile
loudspeakers and custom in-wall installation.
In various other applications there may be a definite
advantage to utilise the benefits of the "infinite baffle"
configuration, without having the luxury of a large closed
volume of air behind the panel. Such applications may also
benefit from an overall thinness and lightness of the
loudspeaker. It is an object of the present invention to
bring understanding to this form of deployment and offer
analytical solutions.
A substantial volume of work supports conventional
piston loudspeakers in various modes of operation,
especially in predicting their low frequency behaviour when
used in an enclosure. It is noteworthy that distributed
mode loudspeakers are of very recent development and as
such there is virtually no prior knowledge of the issues
involved to assist with the derivation of solutions for
similar analysis. In what follows, an approach is adopted
which provides a useful set of solutions for a DML deployed
in various mechanoacoustic interface conditions including
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loading with a small enclosure.
The system under analysis is shown schematically in
F~,gux~e 7 . In this exampl a the front side of the panel
rad_ates into free space, whilst. the other side ~.s loaded
3 wit'.~. an enclc;:ure. This coupled system ray be treated as a
nettuork of velocities and pxessuras as shown in the bloeF
diagram of Figure 8. The components are, from lef~ to
right; the electromechanical driving section, the moda?
system of the panel, and the acoustical systems.
10. The normal ve~.ecity of the bending-wave field across a
v:.bxating panel is responsible for its acoustic radiation.
This radiation in tuxn leads to a reacting force Which
modifies the panel ~=ibration. In the case of a DML
radiating equally from both sides, the radiation impedance,
which is the reacting element, is normally insignificant as
compared with the mechanical impedance of the panel.
However, whey. the panel radiates into a small enclosure,
the effect of acousCic impedance due to its rear radiation
is na longer small, and in fact it Will modify and add to
2Q the scale of the modality of the panel.
This coupling, as shown in Figure 9, is equivalent to
a mechanoacoustica~. closed loop system in which the
reacting sound pressure is due to the velocity of the panel.
itself. This pressure modifies the modal distribution of
the bending wave field which i.n turn has an effect on the
sound pressure response and directivity of the panel.
In order to calculate directivity and to inspect
forces and flaws within the system, it is necessary to
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11
solve for the plate velocity. This far-field sound pressure
response can then be obtained with the help of Fourier
transformation of this velocity as described in an article
by PANZER, J; HARRIS, N; entitled "Distributed Mode
Loudspeaker Radiation Simulation" presented at the 105th AES
Convention, San Francisco 1998 # 9783. The forces and
flows can then be found with the help of network analysis.
This problem can be approached by developing the
velocities and pressures of the total system in terms of
the in-vacuum panel eigen-functions (3,4) as explained in
CREMER,L; HECKL,M; UNGAR,E; "Structure-Borne Sound"
SPRINGER 1973 and BLEVINS, R.D. "Formulas for Natural
frequency and Mode Shape", KRIEGER Publ., Malabar 1984.
For example, the velocity at any point on the panel can be
calculated from equation (1).
~(x,Y) - ~ YPi (J~) ~ Foi (J~) ~ ~Pi (xo~Yo) ' ~Pi (x.Y)
i=0
(1)
This series represents a solution to the differential
equation describing the plate bending waves, equation (2),
when coupled to the electromechanical lumped element
network as well as its immediate acoustic boundaries.
2
~g ~ ~(x,Y) ~- ~' w ' ~(x.Y) - )w' Pm(x.Y) -)~' pa(x,Y)
(2)
LB is the bending rigidity differential operator of
fourth order in x and y, v is the normal component of the
bending wave velocity. a is the mass per unit area and c~
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is the driving frequency. The panel is disturbed by the
mechanical driving pressure, pm. and the acoustic reacting
sound pressure field, pa, Figure 7.
Each term of the series in equation (1) is called a
modal velocity, or, a "mode" in short. The model
decomposition is a generalised Fourier transform whose
eigen-functions ~Pi share the orthogonality property with
the sine and cosine functions associated with Fourier
transformation. The orthogonality property of ~Pi is a
necessary condition to allow appropriate solutions to the
differential equation (2). The set of eigen-functions and
their parameters are found from the homogenous version of
equation (2) i.e. after switching off the driving forces.
In this case the panel can only vibrate at its natural
frequencies or the so-called eigen-frequencies, ~i, in
order to satisfy the boundary conditions.
In equation ( 2 ) , dpi ~x, y~ is the value of the ith plate
eigen-function at the position where the velocity is
observed. ~pi (xo,yo~ is the eigen-function at the position
where the driving force Fpi~~w~ is applied to the panel. The
driving force includes the transfer functions of the
electromechanical components associated with the driving
actuator at (xo,yo), as for example exciters, suspensions,
etc. Since the driving force depends on the panel velocity
at the driving point, a similar feedback situation as with
the mechanoacoustical coupling exists at the drive
point(s), albeit the effect is quite small in practice.
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Figure 10 gives an example of the velocity magnitude
distribution of a single eigen-function across a DML panel.
The black lines are the nodal lines where the velocity is
zero. With increasing mode index the velocity pattern
becomes increasingly more complex. For a medium sized
panel approximately 200 modes must be summed in order to
cover the audio range.
The modal admittance, Ypi~~~,~, is the weighting function
of the modes and determines with which amplitude and in
which phase the itn mode takes part in the sum of equation
(1). Ypi, as described in equation (3), depends on the
driving frequency, the plate eigen-value and, most
important in the context of this paper, on the acoustic
impedance of the enclosure together with the impedance due
to the free field radiation.
Yp i (S, = 1 . Sp ' dpi
2 2
Rpi Sp + Sp ~ dpi + Ypi v
(3)
sp - s/wp is the Laplace frequency variable normalised to
the fundamental panel frequency, mp, which in turn depends
on the bending stiffness Kp and mass Mp of the panel, namely
(~p2= Kp/Mp. Rpi is the modal resistance due to material
losses and describes the value of Ypi~~~,~ at resonance when sp
- ~,pi. ~,Pi is a scaling factor and is a function of the itn
plate eigen-value ~,pi and the total radiation impedance Z",ai
as described in equation (4).
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yp; (S~ = J~p~ + SP ~ Zma i (!w~ .
Kp Mp
(4)
In the vacuum case ( Zmai°O) the second term in equation
(3) becomes a band-pass transfer function of second order
with damping factor dpi. Figure 11 shows the magnitudes of
the frequency response of the in-vacuum Ypi,~W~ for the first
ten modes of a panel, when clamped at the edges. The panel
eigen-frequencies coincide with the peaks of these curves.
If the same panel is now mounted onto an enclosure,
the modes will not only be shifted in frequency but also
modified, as seen in Figure 12. This happens as a result
of the interaction between the two modal systems of the
panel and the enclosure, where the modal admittance of the
total system is no longer a second order function as in the
in-vacuum case. In fact, the denominator of equation (3)
could be expanded in a polynomial of high order, which will
reflect the resulting extended characteristic function.
The frequency response graphs of Figure 13 shows the
effect of the enclosure on the panel velocity spectrum.
The two frequency response curves are calculated under
identical drive condition, however, the left-hand graph
displays the in-vacuum case, whilst the right hand graph
shows the velocity when both sides of the panel are loaded
with an enclosure. A double enclosure was used in this
example in order to exclude the radiation impedance of air.
The observation point is at the drive point of the exciter.
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Clearly visible is the effect of the panel eigen-frequency
shift to higher frequencies in the right diagram, which was
also seen in Figure 12. It is noteworthy that as a result
of the enclosure influence, and the subsequent increase in
5 the number and density of modes, a more evenly distributed
curve describing the velocity spectrum is obtained.
The mechanical radiation impedance is the ratio of the
reacting force, due to radiation, and the panel velocity.
For a single mode, the radiation impedance can be regarded
10 as constant across the panel area and may be expressed in
terms of the, acoustical radiated power Pai of a single mode.
Thus the modal radiation impedance of the ith mode may be
described by equation (5).
Pai
15 Zmai =2' 2
< v; >
(5)
<vi> is the mean velocity across the panel associated
with the ith mode. Since this value is squared and
therefore always positive and real, the properties of the
radiation impedance Z",ai are directly related to the
properties of the acoustical power, which is in general a
complex value. The real part of Pai is equal to the radiated
far-field power, which contributes to the resistive part of
Z",ai, causing damping of the velocity field of the panel.
The imaginary part of Pai is caused by energy storing
mechanisms of the coupled system, yielding to a positive or
negative value for the reactance of Zmai.
A positive reactance is caused by the presence of an
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16 -
acoustical mass. This is typical, for example, of
radiation into free space. A negative reactance of Z"~i, on
the other hand, is indicative of the presence of a sealed
enclosure with its equivalent stiffness. In physical
terms, a 'mass' type radiation impedance is caused by a
movement of air without compression, whereas a 'spring'
type impedance exists when air is compressed without
shifting it.
The principal effect of the imaginary part of the
radiation impedance is a shift of the in-vacuum eigen
frequencies of the panel. A positive reactance of Z",~i
(mass) causes a down-shift of the plate eigen-frequencies,
whereas a negative reactance (stiffness) shifts the eigen
frequencies up. At a given frequency, the pane-mode itself
dictates which effect will be dominating. This phenomenon
is clarified by the diagram of Figure 14, which shows that
symmetrical mode shapes cause compression of air, 'spring'
behaviour, whereas asymmetrical mode shapes shift the air
side to side, yielding an acoustical 'mass' behaviour. New
modes, which are not present in either system when they are
apart, are created by the interaction. of the panel and
enclosure reactances.
Figure 15 shows the frequency response of the
imaginary part of the enclosure radiation impedance. The
left-hand graph displays a 'spring-type' reactance,
typically produced by a symmetrical panel-mode. Up to the
first enclosure eigen-frequency the reactance is mostly
negative. In-vacuum eigen-frequencies of the panel, which
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are within this frequency region; are shifted up. In
contrast the right diagram displays a 'mass-type' reactance
behaviour, typically produced by an asymmetrical panel
mode.
If the enclosure is sealed and has a rigid wall
parallel to the panel surface, as in our case here, then
the mechanical radiation impedance for the ith-plate mode is
(5)
~'(i,x,l)2.
1 O Zmai ° -l' w' Pa ' Ad x,i kz(x,l) . tan (kz(x,l) ' adz )
(6)
yrci,x,i~ is the coupling integral which takes into
account the cross-sectional boundary conditions and
involves the plate and enclosure eigen-functions. The
index, i, in equation (6) is the plate mode-number; Ldz is
the depth of the enclosure; and kZ is the modal wave-number
component in the z-direction (normal to the panel). For a
rigid rectangular enclosure kz is described by equation(7):
2 k.n 2 ~.n
kz(x,l) = ka ( + -
~~dx, ~dY
(7)
The indices, k and 1, are the enclosure cross-mode
numbers in x and y direction, where Ldx and Ldy are enclosure
dimensions in this plane. Ao is the area of the panel and
Ad is cross-sectional area of the enclosure in the x and y
plane.
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Equation (6) is a complicated function, which
describes the interaction of the panel modes and the
enclosure modes in detail. In order to understand the
nature of this formula, let us simplify it by constraining
the.system to the first mode of the panel and to the z-
modes of the enclosure only (k=1=0). This will result in
the following simplified relationship.
A2
ZmaO =-]'Za ' Ao cot (kZ ~~dz)
d
(8)
Equation (8) is the well known driving point impedance
of a closed duct (6). If the product kZ.LdZ « 1 then a
further simplification can be made as follows.
Zmao = A2 .
~'w'Cab
(9)
where Cab = Vb/(Pa.ca2) is the acoustical compliance of the
enclosure of volume Vb. Equation (9) is the low frequency
lumped element model of the enclosure. If the source is a
rigid piston of mass Mms with a suspension having a
compliance Cms then the fundamental 'mode' has the eigen-
value ~,po = 1 and the scaling factor of the coupled system
of equation (9) becomes the well known relationship as
shown in equation (10),[1].
~ + Cms
Cmb
(10)
CA 02326193 2000-09-27
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i,;ith the equi=~a].ent mechanicel compliance of the enclosure
air vvl~~rnc C,;~, = C~b/Ao2.
~'ariou~ tests were carried out to znvestiGate tha
prfect of a sh311o~w back enclosure on DM loudspeakers. zn
addition to bringing general insight ir_to the behaviour ef
pM~, panels in an enclosure, the experi~!ents were designed
to help verify the theoretical model and establish the
extent to which such models are accurate in predicting the
behaviour of the coupled modal system of a DML panel and
lt,s Pnclosuxe.
Two DML panels of d?fferent size and bulk properties
were selected as our test objects. xt was decsded that
these would be of sufficiently different size on the one
hand, and of a useful difference in their bulk groperti.es
on the other, to cover a good range in scale. ~ The first
set 'A' was selected as a small A5 size panel of 149mm x
210mm With three different bulk mechanical properties.
These were AS-1, polycarbonate skin on polycarbonate
honeycomb; A5-2 carbon fibre on Rohacell; and A5-3,
Rohacell withcut skin. Set 'g' was chosen to be eight times
larger, appros~imately to A2 size or 424rcan x 592mm. A2-1
was constructed with glass fibre skin on polycarbonate
honeycomb core, whilst A2-2 was carbon fibre skin on
aluminium honeycomb. Table-1 lists the bulk properties of
these objects. Actuation was achieved . by a sing~,e
electrodynamic t~toving coil exciter at the optimum position.
Two exciter types were used, where they suited most the
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size of the panels under test. In the case of A2 panels a
25mm exciter was employed with B1 - 2.3 Tm, Re = 3.7 ~ and
Le - 60 ~H, whilst a 13mm model was used in the case of the
smaller A5 panels with B1 - 1.0 Tm, Re=7.3 ~ and Le=36 ~,H.
Zm Size
Panel Type (Nm) (Kg/m')(Ns/m) (mm)
A2-1 Glass on PC Core 10.4 0.89 29.3 5 x 592 x 420
A2-2 Carbon on AI Core57.6 1.00 60.0 7.2 x 592 x
420
A5-1 PC on PC core 1.39 0.64 7.5 2 x 210 x 199
A5-2 Carbon on Rohacell3.33 0.65 11.8 2 x 210 x 199
A5-3 Rohacell core 0.33 0 32 2 7 I 3 x 210 x 149
5 I I I I
Panels were mounted onto a back enclosure with
adjustable depth using a soft polyurethane foam for
suspension and acoustic seal. The enclosure depth was made
adjustable on 16,28,40 and 53mm for set 'A' and on 20,50,95
10 and 130mm for set 'B' panels. Various measurements were
carried out at different enclosure depths for every test
case and result documented.
Panel velocity and displacement were measured using a
Laser Vibrometer. The frequency range of interest was
15 covered with a linear frequency scale of 1600 points. The
set-up shown in Figure 16 was used to measure the panel
mechanical impedance by calculating the ratio of the
applied force to the panel velocity at the drive point.
2 0 Zm = F
V
In this procedure, the applied force was calculated
-u~rvcrtr-_w os . 1_ ~ CA 023261 ~~ 2000-09-2 ~1~8U 4G~405-~ +4s as _ Gg
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W0 99I~232 2 PCTIG F39 ~3!O t 04 8
21
from the lump parameter information of the e~cc~~er.
Althour~h panel velocity in itself feeds back into the
electromechanical circuit, its couplyng is quite weak. It
can be shown that for small values of exciter H1, ( 1 -3 Tm) ,
- 5 providing that the driving amplifier output impedance is
low (constant voltage), the modal coupling back to the
- electromechanical system is su~ficiQntly weak to make this
assumption plausible. Small error ariszng from this
approximation was therefore iarnored, Figures 18a to f show
ti-:e mechanical imgedance of the A5-1 and A5~2 panels,
derived from the measurement of panel velocity and tree
applied force measured by the Laser Vibrorzeter. Note that
the impedance minima for each enclosure depth occur at the
system resonance mode.
Sound pressure level and polar response 4f the various
panels Grere measured in a large space of 350 cubic metres
and gated at 12 to l9ms for anechoic -response using MLSSA,
depending on the measurement. Power measurements were
carried out employing a 9-microphone array system, as shown
in Figure 17b and in a set-up shown in Figure 17a. These
are plotted in Figures 19a to d fox various enclosure
depths. System resonance is highlighted by markers on the
graphs.
Polar response of the A5~1 and A5-2 panels 'were
measured for a 28mm deep enclosure and the result is~~-shown
in Figures 20a and b. When compared with the Pour plot of
the free DML in Figure 1, they demonstrate the~significance
of the closed-back DMZ in its improved directivity.
AMENDED SHEET
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2
0106-2000 G B 009901048
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To investigate fur~her the nature and the effect of
enclosure on the panel beraviour, especially at the
combined system resonance, 3 special dig wa$ made to allow
the measurement of the internal pressure of the enclosure
at nine predetermined points as shown in Figure ~1. fhe
microphone was inserted in the holes provided within zhe
back-plate of an .F15 enclosure j ig at a predetermined depth,
while the other eight position holes were tightly blocked
with hard rubber grommets. The microphone was mechanically
1f3 isolated from the enclosure by an appropriate rubber
grommet during the measurement..
Frp;Tc this data, a contour plot was created to shoal the
pressure distribution at system resonance and at eithex
side of this frequency as shown in Figures 22a to c_ The
pressure frequency response was also plotted for the nine
positions as shot~n in Figure 23. This graph eXhlblts good
definition in the region of resonance for all curves
associated with the measurement points within the
enclosure. However, the pressure tends to vary across the
2D enclosure cross-sectional area as the frequency is
increased.
The normal component of velocity and displacement
across the panels was measured with a Scanning Laser
Vibrometer. The velocity and displacement distribution
across the panels were plotted to investigate the behaviour
of the panel around the coupled system resonance. The
results were dccumented and a number of the cases are shown
in Figures 2~a to d. These results suggest a timpanic
AMENDED SHEET
CA 02326193 2000-09-27
WO 99/52322 PCT/GB99/01048
23 -
modal behaviour of the panel at resonance, with the whole
of the panel moving, albeit at a lesser velocity and
displacement as one moves towards the panel edges.
In practice this behaviour is consistent for all
boundary conditions of the panel, although the mode shape
will vary from case to case depending on a complex set of
parameters, including panel stiffness, mass, size and
boundary conditions. In the limit and for an infinitely
rigid panel, this system resonance will be seen as the
fundamental rigid body mode of the piston acting on the
stiffness of the enclosure air volume. It was found to be
convenient to call the DML system resonance, the 'Whole
Body Mode' or WBM.
The full theoretical derivations of the coupled system
has been implemented in a suite of software by New
Transducers Limited. A version of this package was used to
simulate the mechanoacoustical behaviour of our test
objects in this paper. This package is able to take into
account all the electrical, mechanical and acoustical
variables associated with a panel, exciter(s) and
mechanoacoustical interfaces with a frame or an enclosure
and predict, amongst other parameters, the far-field
acoustic pressure, power and directivity of the total
system.
Figure 25a shows the log-velocity spectrum of a free
radiating, A5-1 panel clamped in a frame, radiating in free
space equally from both sides. The solid line represents
the simulation curve and the dashed line is the measure
CA 02326193 2000-09-27
WO 99/52322 PCT/GB99I01048
24 -
velocity spectrum. At low frequencies the panel goes in
resonance with the exciter. The discrepancy in the
frequency range above 1000 Hz is due to the absence of the
free field radiation impedance in the simulation model.
Figure 25b shows the same panel as in Figure 25a but
this time loaded with two identical enclosures, one on each
side of the panel, with the same cross-section as the panel
and a depth of 24mm. A double enclosure was designed and
used in order to exclude the radiation impedance of free
field on one side of the panel and make the experiment
independent of the free field radiation impedance. It is
important to note that this laboratory set-up was used for
theory verification only.
In order to enable velocity measurement of the panel,
the back walls of the two enclosures were made from a
transparent material to allow access by the laser beam to
the panel surface. This test was repeated using panel A5-3
Rohacell without skin, with different bulk properties and
the result is shown in Figures 26a and b. In both cases
simulation was performed using 200 point logarithmic range,
whilst the laser measurement used 1600 point linear range.
From the foregoing theory and work, it is clear that a
small enclosure fitted to a DML will bring with it, amongst
a number of benefits, a singular drawback. This manifests
itself in an excess of power due to WBM at the system
resonance as shown in Figures 27a and b. It is noteworthy
that apart from this peak, in all other aspect the enclosed
DML can offer a substantially improved performance
CA 02326193 2000-09-27
WO 99152322 PCT/GB99/01048 -
25 -
including increased power bandwidth.
It has been found that in most cases a simple second
order band-stop equalisation network of appropriate Q
matching that of the power response peak, may be designed
to equalise the response peak. Furthermore in some cases
a single pole high-pass filter would often adjust for this
by tilting the LF region, to provide a broadly flat power
response. Due to the unique nature of DML panels and
their resistive electrical impedance response, whether the
filter is active or passive, its design will remain very
simple. Figure 28a shows where a band-stop passive filter
has been incorporated for equalisation. Further examples
may be seen in Figures 28b and c that show simple pole EQ
with a capacitor used in series with the loudspeakers.
When a free DML is used near and parallel to a wall,
special care must be taken to ensure minimal interaction
with the latter, due to its unique complex dipolar
characteristics. This interaction is a function of the
distance to the boundary, and therefore, cannot be
universally fixed. Full baffling of the panel has
definite advantages in extending the low frequency
response of the system, but this may not be a practical
proposition in a large number of applications.
A very small enclosure used with a DML will render it
independent of its immediate environment and make the
system predictable in its acoustical performance. The
mathematical model developed demonstrates the level of
complexity for a DML in the coupled system. This throws a
CA 02326193 2000-09-27
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26 -
sharp contrast between the prediction and design of a DML
and that of the conventional piston radiator. Whilst the
mechanoacoustical properties of a cone-in-box may be found
by relatively simply calculations (even by a hand
calculator) those associated with a DML and its enclosure
are subject to complex interactive relationships which
render this system impossible to predict without the proper
tools.
The change in system performance with varying
enclosure volume is quite marked in the case where the
depth is small compared with the panel dimensions. However,
it is also seen that beyond a certain depth the increase in
LF response become marginal. This of course is consistent
with behaviour of a rigid piston in an enclosure. As an
example, an A2 size panel with 50mm enclosure depth can be
designed to have a bandwidth extending down to about 120Hz,
Figure 24.
Another feature of a DML with a small enclosure is
seen to be a significant improvement in the mid and high
frequency response of the system. This is in many of the
measured and simulated graphs in this paper and of course
anticipated by the theory. It is clear that the increase
in the panel system modality is mostly responsible for this
improvement, however, enclosures losses might also
influence this by increasing the overall damping of the
system.
As a natural consequence of containing the rear
radiation of the panel, the directivity of the enclosed
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27 -
system changes substantially from a dipolar shape to a near
cardioid behaviour as shown in Figure 17. It is envisaged
that the directivity associated with a closed-back DML may
find use in certain applications where stronger lateral
coverage is desirable.
Power response measurements were found to be most
useful when working with the enclosed DM system, in order
to observe the excessive energy region that may need
compensation. This is in line with other work done on DM
loudspeakers, in which it has been found that the power
response is the most representative acoustic measurement
correlating well to the subjective performance of a DML.
Using the power response, it was found that in practice a
simple band-pass or a single pole high-pass filter is all
that is needed to equalise the power response in this
region.
