PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

HiFi Panel Speaker by Controlling the Vibration Field Using ArrayActuators
Ki-Ho LEE1; Jeong-Guon IH21, 2

Korea Advanced Institute of Science and Technology, Korea

ABSTRACT
Most of panel speakers adopt a thin rectangular plate, which is excited by one or several actuators. Becauseof the multi-modal characteristic of the plate, the vibration field composed of many modes deteriorates theradiated sound quality inherently, in particular at the low to medium frequency range. This study deals withthe control of a point-excited panel speaker to radiate HiFi and powerful sound using an actuator arrayenclosing the main actuator zone. The desired control is to confine the major in-phase oscillation at aroundthe main actuator and to suppress the vibration in the remainder area, resulting a virtual circular speaker anda baffle. The gain of actuators is obtained by solving the inverse rendering problem derived from the transfer
function between the actuator input and the response of field point on the plate. Two types of array
configurations are investigated by simulation, which shows that the adjacent double circular array canproduce the sound radiation for a wide frequency band. The experiment conducted using the double circulararray reveals that the vibration field can be controlled well as desired and the present control method canimprove the frequency response drastically to be flat.
Keywords: Panel speaker, inverse rendering, vibration control, array actuators, radiated sound

1. INTRODUCTION
Flat panel speakers often adopt a thin rectangular plate as the radiator excit ed by one or several
actuators. Due to the multi-modal characteristic of the plate, however, the resultant vibration field is
usually contributed from many modes. Such complicated vibration field deteriorates the radiatedsound quality inherently, especially at the low to medium frequency range, and the radiation efficiency
is low. So, it is important to control the vibration field of the panel speaker to make it a HiFi radiator.
In this study, the desired vibration field is a system which is a combination of a circular piston and abaffle, radiating desired sound power. The basic concept is shown in Fig. 1. The control actuator arraysurrounding the main actuator is configured to generate the desired field. The inverse rendering
technique is adopted to obtain the proper complex gain of control actuators.
(a)

(b)

(c)

Figure 1 – Schematic of the concept of the vibration field control for the rectangular panel speaker: (a)initial field by main actuator, (b) target field for control actuators, (c) desired ideal field.

2. FIELD CONTROL USING AN ACTUATOR ARRAY IN DOUBLE LAYERS
To convert the initial field due to the main actuator into the desired field after control, the inverse
problem should be set using the transfer function between the input force of each control actuator andvelocity response of each field point on the plate. The vibration field of an infinite plate excited by a126316k.h.lee@kaist.ac.kr
J.G.Ih@kaist.ac.kr

point force can be expressed by travelling wave form (1) asv r; ZF0Z
ª H 02 kB r  H 02  jkB r º ,¼8BkB2 ¬(1)

where r is distance between excitation point and field point, F0 the excitation force, B the bending
rigidity, and k B the bending wave number. On the other hand, the vibration field of a finite plate excitedby a point force can be defined by the mode summation method (2, 3) as follows:
v x, y; Z

jZ\ i x, yf¦
i 1^Z 1  jK  Z `^³ U h\2i

2i

S

p2i

`³x, y dxdy

S

F0G xn , yn \ i x, y dxdy .

(2)Here, ߰ is the mode shape function, i the index of the i th vibration mode, ߟ the loss factor of theplate, ߩp the plate density, and h the thickness of the plate.
In this work, Eq. 2 is to be used for deriving the transfer function, assuming that the steady-statevibration field is considered for a finite plate. Nevertheless, it is also important to look into thevibration field in travelling wave form of Eq. 1 to investigate the wave propagation invoking thecontrolled field. By using Eq. 2, the target vibration field to control the initial field is defined asif ( xm , ym )  speaker zoneªT  v0 xm , ym ; Zvt xm , ym ; Z «,(3)
if ( xm , ym )  baffle zone
¬ v0 xm , ym ; Z
where T is the desired velocity of the speaker zone, v0 the initial field by the main actuator, and vd thedesired vibration field to be generated on the plate. When Eq. 3 is expressed in a matrix form withrespect to the field points and the input gain of control actuators, one can obtain the actuator gain togenerate the desired field by solving the inverse problem (2-4) as follows:(4)
Vt GF o F=G†Vt .
Here, F is the vector consisting of actuator gain, G is the transfer matrix between the gain of actuatorsand the velocity response at field points, and the superscript ˋG denotes the pseudo inverse operator.
Tikhonov regularization is additionally applied to secure the stability of the solution (5, 6).

3. EFFECTIVE FREQUENCY RANGE FOR SOUND RADIATION
3.1 Simulation set-up
A simply supported aluminum plate with a size of 700 mm x 400 mm x 2 mm is chosen as the plate
for the test. A main actuator attached to the plate center excites a unit force within the freque ncy rangeof 50-1000 Hz. Control actuator arrays configured in the double layer are shown in Fig. 2. The inside
area of the inner array is defined as the speaker zone and the remaining area as the baffle zone. Thedesired velocity of the speaker zone is determined to radiate 80 dB of sound power.
3.2 Determination of Effective Frequency Range
For the effective sound radiation, the speaker zone should have velocity field with the desired
magnitude and uniform phase distribution. On the other hand, the velocity field of the baffle zone
should be no larger than the tolerance value. The tolerance value is determined by a criterion on thedesired difference in sound power radiation contributed from each zone. In this work, it is set to belarger than 15 dB, for the worst condition of uniform phase distribution. The velocity error magnitude
compared to the desired field can be defined as
(a)

(b)

Figure 2 – Actuator array configured in double layer: (a) double circular array, (b) circular array and edgearray located at the periphery of the plate.

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espkT  vspk

vtol  vbff / vtol .

T , ebff(5)Here, v tol is the velocity tolerance of the baffle zone and ‫ݒ‬ҧ the spatially averaged velocity. Figure 3
shows the velocity magnitude error and the standard deviation of phase distribution in the controlled
field when the diameter of speaker zone is 0.18 m. One can find that the double circular array has
smaller error than the circular and edge array. The error in the baffle also reveals that the double
circular array is the best in making a satisfactory baffle zone. From the baffle zone result, the lower
limit of the effective frequency range can be determined. Considering the sound power radiation, it isfound that the variation of the sound power is less than 3 dB when the standard deviation of velocity
phase is less than 20 o. Based on this criteria, the high limit of the effective frequency range is selected
for each array configuration. As a result, the effective frequency range of each array configuration isdetermined varying the speaker zone diameter as shown in Fig. 4. One can observe that the circularand edge array has the effective frequency range only for the speaker diameter in the range of 0.240.28 m. If the 15 dB criterion is relieved to 10 dB, the ranges become wider.
(a)

(b)

Figure 3 – Result of velocity magnitude error and phase distribution in the speaker and baffle zone: (a)velocity magnitude error, (b) phase distribution.
(a)

(b)

Figure 4 – Frequency range for effective sound radiation: (a) double circular array, (b) circular and edgearray.

4. MEASUREMENT OF TRANSFER FUNCTION
4.1 Experimental Set-up
To validate the vibration field control method suggested in this work, an experiment is conducted
for the test plate under the same condition with the simulation. However, the actual boundary
condition would be a bit different from the ideal simply-supported one. The double circular array isconfigured with 31 control actuators (Tectonic, TEAX14C02-8) and a main actuator (Dayton Audio,DAEX25FHE-4), which is attached to the geometric center of the plate. The vibration field ismeasured using laser vibrometer (Polytec, OFV 056) at 325 observation points on the plate. The
transfer function for the control is determined by using the measured velocity response at eachobservation point and the input voltage signal of each control actuator.

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4.2 Result of Vibration Field Measurement
The measured frequency range of interest is 200-570 Hz considering the resonance characteristicof the actuator and modal overlap of the test plate. To investigate how much the speaker and baffle
zones are generated as intended, the sectioning performance (SP) is defined as follows:
SPEspk Etotal2§·¨ ³S v Z dS ¸© spk¹

³ vZS2dS .

(6)

Eq. 6 means the ratio of the vibration energy concentrated in the speaker zone to that of the total plate
and the result is shown in Fig. 5(a). Compared with the initial field by a main actuator only, one cansee that the most of vibration energy is concentrated in the speaker zone by the control. Figure 5(b)shows the sound power radiated from the plate. After the field control by the actuator array, the power
spectrum become flattened and the magnitude is enhanced satisfying the desired value of 80 dB.
(a)

(b)

Figure 5 – Experimental result of vibration field control: (a) sectioning performance, (b) estimated soundpower radiation from the controlled vibration field

5. CONCLUSIONSIn this study, the vibration field of a panel speaker excited by a main actuator is controlled by using
an array of control actuators arranged in the double layered configurations. The control performanceof two types of control actuator array is simulated, and the effective frequency range for the soundradiation is determined for each array. It is noted that the double circular array has much wider
effective frequency range than the circular and edge array. An experiment to validate the proposed
control method shows that the vibration energy is concentrated within the speaker zone as desired by
the control. The sound power radiated from the controlled vibration field reveals that the severe
fluctuation in sound spectrum of the initial field is flattened and the overall magnitude is also enhanced
to fulfill the desired value. Consequently, it is shown that the resultant sound field does not include
the distortion, resulting an improved sound quality, owing to the control by control array.

ACKNOWLEDGEMENTS
This work was partially supported by the BK21-Plus Project and the NRF grants (No.
2016K2A9A2A12003779 and No. 2017R1A2B4007133).

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5. Tikhonov A, Arsenin V. Solutions of Ill-Posed Problems. New York, USA: Wiley; 1977.
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