2012 2nd International Conference on Computer Design and Engineering (ICCDE 2012)
IPCSIT vol. 49 (2012) © (2012) IACSIT Press, Singapore
DOI: 10.7763/IPCSIT.2012.V49.18
Analysis of Edge Boundaries in Multiactuator Flat Panel
Loudspeakers
B.Pueo 1 + and J.J. López 2
1
2
Computing ServiceCommunication and Social Psychology Dept.Universidad de Alicante, Spain
Instituto de Telecomunicaciones y Aplicaciones MultimediaUniversidad Politecnica de Valencia, Spain
Abstract. Multiactuator Panels (MAPs) consist of a light and stiff flat panel to which several mechanical
exciters are attached in order to create bending waves that are radiated as acoustic wave fields. MAPs are
typically used as an alternative to traditional dynamic loudspeaker arrays for a surround sound technique
known as Wave Field Synthesis (WFS) with distinct advantages, such as the low visual profile or
omnidirectional acoustic radiation. However, the panel edge boundary conditions are of critical importance to
acquire the desired sound field, as in the rest of transducing techniques. In this paper, the structural acoustic
behavior of a MAP loudspeaker prototype is measured and simulated for two classical edge boundary
conditions: free and clamped. Special attention has been made in the interaction between exciters sharing the
same vibration surface and the role that their position would play in the sound-generating behavior of the
panel for WFS applications.
Keywords: Acoustics, Loudspeaker, Panel, Boundary condition, Exciter
1. Introduction
Wave Field Synthesis (WFS) is a surround sound technique aiming at the creation of a true acoustic field
by means of closely spaced loudspeaker [1], [2]. Each loudspeaker contributes to form an acoustic wave
front which is perceived by the audience as if the synthetic sound is really there. The best results are acquired
when an area is completely surrounded by loudspeakers which create a volumetric velocity proportional to
the normal particle velocity component of the original wave front. Many transducing mechanisms have been
used in loudspeaker arrays to form WFS systems during the past years. For practical purposes, there are two
sort of loudspeaker arrays. First, the ones based in dynamic transducing, which have comprehensively been
described in the technical literature and are of common use in audio systems. Second, flat lightweight panel
loudspeakers known as Distributed Mode Loudspeakers (DML) [3] that enables the creation of mechanical
waves with attached exciters. The acoustic radiation of DML panels is made by bending waves that travel
across their surface [4],[5].
Multiactuator Panels (MAPs) are a step forward of the distribute mode technology which aim is to be
used in WFS applications [6]. Contrary to DMLs, MAPs comprise of a set of exciters on a single vibrating
surface. MAPs exhibit several benefits: they can easily be incorporated into living rooms since its visual
profile is very low and the surface vibration is almost negligible so that it can be used as a projection screen
[7]. In a complex vibrating surface such as the MAP panel, the intrinsic characteristics of panel radiation
must not deteriorate the desired synthetic wave field under WFS. The MAP panel vibrates in a complex
pattern over its entire surface due to the simultaneous mechanical excitations of a number of transducers.
Additionally, there are some specific locations to excite efficiently a panel but exciters in a MAP are no
longer located in optimal positions, but evenly distributed on a line according to the requirements of the
+
Corresponding author. E-mail address: basilio@ua.es.
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WFS algorithm [8]. On the other hand, each exciter on the panel should generate a well-defined point-source
like radiation, acting as an individual loudspeaker channel [9]. Furthermore, in a practical MAP arrangement
for WFS, the edge exciters on a panel are located very close to the panel boundaries so as to ensure a evenly
spaced continuous distribution of exciters [10].
In this paper, the impact that different edge boundary conditions has on the structural performance of the
panel is study by observing the surface velocity over the whole area of a MAP prototype. For that purpose,
the vibration of the panel by means of mechanical exciters at WFS locations with audio signals is studied
under two edge boundary conditions with the same panel and housing: free and clamped. The latter is a type
of edge condition that ensures robustness that has been used in practical clamping mechanism in real-world
MAP implementations.
2. Multiactuator Panels for Wave Field Synthesis
Wave field synthesis (WFS) is a spatial sound field rendering technique that employs a large number of
loudspeakers to generate a virtual auditory scene over a large listening space. WFS overcomes some of the
limitations of stereophonic reproduction techniques, such as the sweet-spot [11]. The theoretical background
of WFS was firstly formulated by Berkhout et al. at the Delft University of Technology almost 20 years ago
[1], in which they developed WFS as a direct application of the Huygens’ principle [12]. According to this,
with loudspeaker arrays, acoustic wavefronts can be synthesized within a volume. Each loudspeaker of the
array performs as a secondary source and the entire system synthesize a sound field created by one or some
sources placed behind the loudspeaker array. According to the Huygens’ Principle, the sound field inside a
source-free volume can be calculated if the pressure field due to the primary sources on the enclosing surface
is known. The driving signals of the loudspeakers have to be weighted and delayed to accomplish the
degeneration from an arbitrary surface to a line throughout the Kirchhoff-Helmholtz integral.
However, the practical application of WFS is a difficult task. There are some shortcomings of this
system, such as the large number of loudspeakers required and the high computational cost of generating a
dedicated signal for each of the loudspeaker. This disadvantage is however getting solved nowadays due to
the rapidly changing technology. When implement a WFS system, the most common way is by means of
dynamic loudspeaker drivers. However, these transducers show a key disadvantage as they need housing
with a moderately large volume to avoid additional stiffness that would ruin the low frequency band of the
driver. In addition, the piston-like motion of their diaphragms makes them to exhibit strong and narrow lobes
around their main axis at high frequencies [13].
Due to the limitations that the use of dynamic loudspeakers has revealed, the aim was to find alternatives
that were as omnidirectional as possible, light-weight and easy to be unnoticed on a wall surface. Therefore,
the applicability of Distributed Mode Loudspeakers (DML), which show these advantages, as substitute for
WFS reproduction was investigated [6]. A DML basically consists of a thin, rigid panel in a small backvolume that vibrates in a complex pattern by means of an electro-mechanic transducer called an exciter.
Although DML could be used successfully for WFS, small panels posed some problems with sound quality
since they have a poor low-frequency response due to the lack of excited low frequency modes. Therefore,
this technology was applied to a large panel with multiple exciters, each driven with a different signal. This
configuration was later named MAPs to distinguish them from the single-excited panels [9]. A MAP would
act as a WFS array if every exciter on the panel drives only a small portion of the panel around its location
and therefore, each exciter can receive a different signal without the interference of adjacent exciters [14].
3. Experimental Setup
A large MAP prototype was built at the laboratory with the aim of serving both as a loudspeaker and a
projection screen. The prototype dimensions are similar to a 100 inches widescreen (244 x 122 cm) that
enabled designers to distribute a total of 13 exciters spaced 18 cm apart on the horizontal plane. This
distribution facilitates an aliasing-free emission up to approximately 1 kHz. A supporting set of exciters were
provided both above and below the central array for assessing the impact of boundaries in exciters very close
to edges. The panel is a 5 mm sandwich that connects a thermoplastic outer skin material to a polycarbonate
inner honeycomb core. The panel bending stiffness is 16.4 and 16 Nm in the x and y directions respectively
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and has an areal density of 0.89 kg/m2. The exciters are 25 mm diameter dynamic transducers with an eightfoot panel coupling. Two different ways of supporting the panel are simulated. Rectangular plates are
generally classified in accordance with the type of support used [15]. The ideal free condition (F) implies
that the structure is floating in the air without support of any kind. To satisfy this condition, no reaction
forces must arise along the edges. On the other hand, the clamped condition (C) is attained by grounding the
structure with well-tightened procedures that avoid the deflection of the structure at the supports. Simulations
were conducted using a finite element solver to obtain the field distribution of velocity values over the MAP
panel. The experimental structural analysis of the panel was performed by measuring the transverse surface
velocity impulse response with a Laser Doppler Vibrometer on a 1 x 1 cm rectangular grid over selected
areas.
4. Results and discussion
4.1. Interaction with Boundaries
For WFS purposes, it is advisable for each exciter to create a well-defined wave front, regardless of the
initial pseudo-random behavior. For assessing the impact that a reflection edge boundary such as the
clamped boundary condition, a set of experimental measurements with laser vibrometry were conducted. The
aim was to show the differences in pulse formation as a function of the location of the exciter. For that
purpose, three significant exciters were measured at 40 ms from the origin of the pulse: central, lateral and
corner areas, as depicted in Figure 1, in a grid with spatial resolution of 2 cm in both directions.
Figure 1(a) depicts the pulse in an area where no edges surrounding can interact with the wave
propagation. Therefore, bending waves have no disturbance when traveling across the panel. In Figure 1(b),
the exciter behavior is shown when placed near one edge, illustrated as a gray wall in the representation. A
slight reflection can be observed in the vicinity of the exciter, hence the boundary proximity play a role in
the pulse propagation, as expected. Lastly, the behavior of the corner grid is presented in Figure 1(c), with a
grid resolution of 1 cm for better analysis. The boundaries both in horizontal and vertical directions are
illustrated by two gray walls adjacent to the exciter position. This scenario is not advisable for WFS since the
exciter moves the panel in a location well constrained by boundaries in two directions. Therefore, the pulse
close to boundaries has changed its shape from spherical to lineal due to the neighboring effect. However,
the pulse opposite to boundaries shows the expected spherical traveling wave.
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Fig. 1: Experimental velocities at 40 ms for a large MAP with clamped boundaries in three representative locations: (a)
central, (b) lateral and (c) corner.
4.2. Interaction with Boundaries
The previous results indicate that boundaries play a role in the formation of the pulse. In this section, the
requirement for each exciter to behave as a point source is examined for both boundary conditions. The pulse
response of the panel surface over the transducer has to be as shorter as possible. Although the signal driven
to the panel is inevitably transmitted along the whole surface, maximum values are found, generally, around
the exciter area for the first instants of time. For that reason is important that each transducer excites a small
area around its position for the first instants of time where the maximums values of energy are conveyed to
the panel. To study the interaction between exciters, and that the area driven by them is sufficiently small to
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behave as point sources, some simulations were made. Figure 2 shows the behavior of the five central
exciters when they are fed with equal and counterphase signals to create an acoustic wave.
Exciters driven by signals in counterphase
Exciters driven by the same signal
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Fig. 2: (a) MAP velocity impulse response snapshot at t=0.02 s with the five central transducers with clamped edge.
(b) MAP profile from simulation (c) MAP profile from free edges.
For drivers with the same signal, Figure 2(a) indicates graphically that each exciter has its own well
defined excitation area. For this time step, when the energy of the pulse is being spread, regions of maxima
velocity are clearly seen as well as areas with an insignificant velocity compared to the exciters position.
These locations with low velocity set a valley between excitation areas. As far as these areas have a
minimum extension along the horizontal axe, no interaction between exciters will be created. That means
that energy of the reproduction signal will be delivered to the panel with no cross-talk. To illustrate the shape
mentioned above, in Figures 2(b) and (c) the panel profile has been represented for clamped and free
configurations, respectively. Notice that the free configuration shows larger excitation areas and therefore the
appearance of cross-talk since the valleys raised establishing an offset, in dashed line in the graphs.
The next study performs the worst scenario which may occur in WFS when a tangential plane wave is
reproduced. Examining the left side of Figure 2(a), the same conclusion as in the previous experiment can be
formulated. No cross-talk will occur with a distance between exciters of 18 cm. Again, the valleys for
clamped edge can be perfectly observed between driving areas, as shown in Figure 2(b). However, for the
free boundary condition illustrated in Figure 2(c), cross-talk will not appear as an offset but a tension area of
the panel instead of distended valleys.
5. Conclusion
A simulation study of both the impact that edge boundary conditions have on the structural behaviour of
MAPs and the interaction between the exciters coupled to the panel, have been presented in this paper. Two
different edge configurations of a MAP prototype built in the laboratory have been simulated in order to
analyze the acoustical behavior for WFS applications. For Free configuration, the energy in the panel,
applied by the exciters, is attenuated more slowly than in other configuration because bending waves have no
resistance when they travel across the panel. Such a configuration allows the panel edges to reach velocities
values comparable to the exciters ones or even higher hence, some parts of the panel will act as low
frequency sound sources interfering significantly with the signals coming from the exciters. Therefore,
regarding the applicability of this boundary condition for WFS reproduction, this configuration is not
suitable as the localization of the sound sources will be partially incorrect. For Clamped configuration there
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are some panel areas which reach velocities comparable to the main pulse although this phenomena occurs in
a much smaller proportion than for the Free configuration. The main causes of the energy dissipation are the
collision with the clamped edges and the cancellation resulting between reflected waves. The experimental
velocity values, collected with a LDV, demonstrate that for the three zones under test the maximum
velocities are originated around at the exciter location. For lateral and corner areas, all the reflecting behavior
due to the proximity to boundaries are of very small energy compared to the initial pulse. Therefore, the
clamped boundary condition applied to this MAP loudspeaker allows each exciter to move a small area
around its location for the first milliseconds of time with a deterministic signal provided by the WFS
application.
6. Acknowledgements
This work has been supported by Spanish Ministry of Science and Technology (MCYT) under Project
ref. TEC2009-14414-C03-01, by the University of Alicante under Project ref. GRE09-33, by Generalitat
Valenciana under Project ref. GV/2011/042 and FEDER funds.
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