Active control by using optical sensors on the acoustic radiation from square plates

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Applied Acoustics 69 (2008) 367–377 www.elsevier.com/locate/apacoust

Active control by using optical sensors on the acoustic radiation from square plates K.T. Chen *, S.H. Chang, C.H. Chou, Y.H. Liu The Institute of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sect. 4, Roosevelt Road, Taipei, Taiwan, ROC Received 27 July 2006; received in revised form 17 October 2006; accepted 20 November 2006 Available online 11 January 2007

Abstract This study is reported of an optical approach to reduce the acoustic radiation from some uniformly square plates of different sizes. The content of this study includes the dynamical analysis of uniform plates, the theoretical consideration dealing with both the opticalerror path and neural network control system, and the laboratory demonstration on the acoustic-radiation reduction from plates by using optical approach. Results of dynamical analysis on three different plates obviously reveal low odd–odd modes such as (1, 3) and (3, 3) mode must respond to the most acoustic radiation from plates. Laboratory demonstration claims that much more reduction of acoustic radiation from plates within greater frequency range can be reached when using an optical-error path to replace acoustic-error path. The corresponding experimental results obviously show that the greater control effectiveness on (3, 3) mode for smaller plate, single frequency, the greater effectiveness by 26 dB of acoustic radiation reduction for single point control than that for multi points control. Regarding to the double frequencies, the acoustic attenuation by 14.6 dB for compose of (3, 3) and (3, 4) in 60 cm plate are obtained. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Optical error path; Acoustic radiation; Neural-network control; Square plate

1. Introduction Plate structure is a very important component to the most architectural structures, the produced vibration under a periodic external force and the accompanying sound radiation were widely discussed in some past studies [1–3]. Two methods, including a passive and an active technique, are used to control the sound radiation from plates in vibration. Between them, a passive control technique uses sound-protection or sound absorption material in the acoustic transmission path to eliminate the acoustic energy. Alternatively, using refashioning technology [2,3] can change the dynamical characteristics of plates and then reduce the sound radiation from them.

*

Corresponding author. Tel.: +886 2 336 65744/936 815 491; fax: +886 2 336 65757. E-mail address: [email protected] (K.T. Chen). 0003-682X/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2006.11.006

Regarding to the active control technique for the acoustic attenuation, it was firstly proposed by Lueg [4] in 1936. Applying the same concept to control the object in vibration can reduce both the resulting amplitude of vibration and the associated sound radiation [5]. In 1991, Clark [6] used a piezoelectric polymer as a sensor to combine with an adaptive control algorithm for reducing the sound radiation from structures. After the study by Clark, the piezoelectric materials were widely used for the vibration control in structures [7,8]. Speaking to the sensor dealing with sound reduction, Fuller [9] placed a microphone in acoustic far field, and then actively controlled to the least extent the plane wave transmission through a simply supported circular plate. Thereafter, the acoustic microphone plays a momentous role in some fields involving in noise control. Alternatively, using the modern development of the properties and theories in optical materials, the associated techniques were widely applied to many fields including the transmission

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of data in communication, the holography technique to display the modes of object, and the combination of optics with microelectronics such as the optical pick-up of DVD player is involved [10–13]. There are well-developed optical sensors such as AVID (Advanced Vibrometer Interferometer Device) or LDV (Laser Doppler Vibrometer); both have superiority of measurement in the surface vibration. The AVID measurement range is limited to maximum translation ranges of the built-in stages [14], we cannot apply to the bigger sample. The LDV is so expensive that we cannot afford. We will propose the best economic benefits optical sensor system which can provide a great effect. In this study, the concept of optical error path comes from the pick-up in DVD player. By this, when laser beams impinge upon a vibrating plate, the resulting optical path will be changed for different amplitude of plate, and the associated signals received at photo sensor can be used as the error signals for the acoustic-radiation control. The results from laboratory measurement obviously reveal that the sound radiations from uniform plates of three different sizes at several frequencies from 100 to 643 Hz are greatly reduced, and the poor effectiveness using microphone as error sensor at higher frequencies is greatly improved as well. 2. Theoretical considerations 2.1. Dynamic analysis of and radiation power from a uniform squared plate Upon the neglecting of shear and torsion deformations, the displacement w(x, y, t) of an un-damped square plate acted on by an external force f(x, y, t) must satisfy the following equation [15]: Dr2 r2 wðx; y; tÞ þ qs h

o2 wðx; y; tÞ ¼ f ðx; y; tÞ ot2

ð1Þ

where $2 is the Laplacian operator, D = Eh3/12(1  m2) and qs are the bending stiffness and bulk density of plate, and hh, E, m are, respectively, its thickness, Young’s modulus and Poisson’s ratio. Using the method of separation variables and the principle of modal analysis can solve Eq. (1) to have solution as n X /i ðx; yÞW i ðtÞ ð2Þ wðx; y; tÞ ¼

modes like (1, 3) or (3, 3) will be much more efficient in acoustic radiation around natural frequency than that of the other modes. When a plate is harmonically excited by a PZT, the vibrating surface will radiate acoustic wave to the surrounding. From the result in Johnson’s study [17], the net volume velocity produced from a plate can be expressed as the sum of its surface velocity and the velocity vc produced by a PZT actuator controller with unit moment. As discussed, the resulting motion of harmonically excited plate is still vibrating harmonically with surface displacement w(x, y)ejxt. We can express the net volume velocity on the plate surface as [18] Z ly Z lx V total ¼ jx wðx; yÞ dx dy ð3Þ 0

Meanwhile, the acoustic pressure radiated from a vibrating plate at some point in far field can be approximated by Rayleigh integral as Z Z jxqejkr ly lx pðr; h; /Þ ¼ jxwðx; yÞejðkx xþky yÞ dx dy ð4Þ 2pr 0 0 The comparison of Eq. (3) with Eq. (4) concludes the acoustic pressure at far field could be proportional to net volume velocity of plate. Therefore, reducing the acoustic pressure should be the same thing as attenuating the acoustic power radiated form the plate. 2.2. Architecture of neural network 2.2.1. Neural network theory This study adopts an error back-propagation neutral network combining with appropriate algorithms. In comparison with adaptive filter, the neutral network is superiority performance in pattern recognition and modeling of nonlinear systems. The structure of network is shown in Fig. 1, its description to back-propagation neutral network to be adopted. By the similar derivation to that of Fukuda’s study [19], the output of neuron in the output layer as shown in Fig. 1 can be expressed as yj = f(netj). Here, f is the activation function of P neuron, which is a hyperbolic function in this study,netj ¼ k ðwkj hidk Þ þ hj is the input of jth neuron, wkj and hj are the associated weighting

θ1

i¼1

The /i(x, y) is the shape function dealing with different boundary condition, Wi(t) is the generalized displacement, and n is the number of the truncated modes to compose the approximate solution to be required. Following Elliott’s study [16], the first radiation mode at low frequency of a uniform plate will have almost constant radiation efficiency and contributes the most of radiation power from plate when it is excited by an external force. Moreover, following Yeh’s study [15], it obviously concluded that most odd–odd

0

θ2

θh

θj

Output layer j

Input layer i Hidden layer h Fig. 1. Error back-propagation neural network.

K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377

parameter and bias. Furthermore, P hidk = f(netk) is the output of hth neuron, netk ¼ k ðwih  xi Þ þ hk is its corresponding input, and, hj are the associated weighting parameter and bias. Generally, the real output uj of a neutral network is always not equal to its desired output tj; the error function between them can be defined as 1X E¼ ðtj  uj Þ ð5Þ 2 j

369

Using the steepest gradient method combining with the error back-propagation algorithm can minimize the error function in Eq. (5). According to Ref. [20], derived from Chain rule and the partial differentiation of adjustable parameters, we know either the modified weighting coefficients or the associated bias at any instant t + 1 from the hth neuron in hidden layer to the jth neuron in the output layer can be expressed in terms of those ones at earlier time t as

from a plate. Using the desired response t as input to the network, the network is adjusted to produce the plant input y that drives the system output f to approach the desired response t. The difference between them is the error function e. The system output depends on error function e. As shown in Fig. 2, N is an excited source; S is a controllable source. D is an error signal to adjust the output of control system; its measure is based on photodetector. Photodetector is constructed of silicon photodiode. Following Toomas’s study [21], the responsivity of photodetector relies on the optical power. Therefore, if responsivity is constant, the photodetector is defined to be linear, in other words, when the optical power affects the responsivity, it is defined as nonlinearity. In this proposal, the responsivity is nonlinearities because the change of the illuminate optical power follows the vibration amplitude of plate. Consequently, as the advantages mentioned above, neutral network is the best vibration control system.

whj ðt þ 1Þ ¼ whj ðtÞ þ g  dj  hidh

ð6Þ

2.3. Optical system theory and application

wih ðt þ 1Þ ¼ wih ðtÞ þ g  dh  x

ð7Þ

hj ðt þ 1Þ ¼ hj ðtÞ  g  dj hh ðt þ 1Þ ¼ hj ðhÞ  g  dh

ð8Þ ð9Þ

where g is the learning rate of the neural network, and dj,h = (tj,h  uj,h)(1 + uj,h)(1  uj,h). 2.2.2. Acoustic power radiation control system Neural network with neuron components can be either a feed forward network or a feed back network. Through the modification of the weighting coefficients of neutral network, we can minimize the difference between the desired output and the plant response. Therefore, we can apply this system to the active control of the acoustic power radiation Plate S

f

D N Neural Network Control System

y

x

e=t-f

t +

-

Fig. 2. The sketch of active control system in plate.

2.3.1. Optical path and displacement of plate By using a far-field microphone as the error signal sensor, most acoustic power radiation control techniques [16,18] adopt volume velocity cancellation method to control the vibration in plate. However, in an anechoic chamber, it still has reflection from it walls. Therefore, the acoustic pressure at far-field and the net volume velocity of plate will not have relations as defined in Eqs. (3) and (4). To improve the drawback as described, we replace error microphone by a laser source and optical sensors. As regards to laser source, it has advantages of good interference, coherence, and small source area for measurement [22]. In this study, we relate optical path of laser light to the displacement of vibrating plate by using laser triangulation method [23]. As shown in Fig. 3, a laser source is fixed at S and a photo detector is placed at P1, which is in the active area. When a collimated laser beam is incident on a static surface with angle hI, the corresponding optical path is SO þ OP . When the plate is vibrating with displacement w1, the laser beam illuminates at O1, the optical path becomes SO1 þ O1 P 1 , and the resulting displacement of plate becomes w1 ¼ ðSO1  SOÞ. Therefore, we still can use volume velocity cancellation method by replacing farfield microphone by some optical components to effectively reduce the acoustic power radiation from a plate. 2.3.2. Plate displacement and photodetector output Again as shown in Fig. 3, the displacement of vibrating plate is directly proportional to both the optical path and its associated optical signal received at photodetector, which can be transferred into the associated electric voltage. If the plate in vibration has maximum displacement, the corresponding irradiance of the photo detector per square millimeter will reach maximum. Otherwise, the reflected illuminating beam is just a part of active area

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Si photodioee Active area φ = 1mm

Laser S

P p2 p1

θi θr

Vibrating Plate

w2 w1

o

o2

V

w1

V1 V2

w2

mW mm2

o1

Fig. 3. Optics path and laser triangulation method.

corresponding to a less voltage output. Therefore, we can regard the output voltage as described as the error signal in the control system. Upon the above error signal, the control system can adjust the output to approach the desired one. 3. Experiments Three square steel plates with constant thickness of 1 mm and different widths of 30 cm, 60 cm and 86 cm are selected to be the test sample for this study. All the plates involved are, respectively, clamped on a heavy cast iron frame when making the associated experiment in progress. To drive a uniform plate to vibrate, a mini-type PZT used as an exciter is affixed to its surface at some appropriate positions. Again, another same type PZT used as a controller is affixed at another position to produce a destructive displacement for reducing both the resulting displacement of plate and the acoustic radiation from its surface. In addition, the experiment will be making in progress at single and double controllers. Table 1 Three square steel plates position of excite point, single control point and double control points, respectively Size (cm2) 30*30

Exciter position (7.5, 7.5)

Error signal position (5, 5)

Mode

Single controller

Double controller 1

2

All mode

(24, 25)

(21, 15)

(21, 15)

60*60

(21, 21)

(17, 17)

(1, 2) (2, 2) (1, 3) (2, 3) (1, 4) (3, 3) (2, 4) (3, 4) (1, 5) (2, 5)

(11.5, 11.5) (11.5, 11.5) (11.5, 11.5) (11.5, 11.5) (21, 21) (48, 48) (11.5, 11.5) (11.5, 11.5) (11.5, 11.5) (11.5, 11.5)

(11.5, 11.5) (26, 26) (26, 26) (11.5, 11.5) (26, 26) (26, 26) (11.5, 11.5) (11.5, 11.5) (11.5, 11.5) (11.5, 11.5)

(48, 48) (48, 48) (48, 48) (48, 48) (48, 48) (48, 48) (48, 48) (48, 48) (48, 48) (48, 48)

86*86

(20, 20)

(16, 16)

(2, 2) (1, 3) (2, 3) (1, 4) (3, 3) (2, 4) (3, 4) (1, 5) (2, 5)

(12, 12) (30, 30) (30, 30) (30, 30) (40, 40) (12, 12) (12, 12) (12, 12) (64, 64)

(12, 12) (30, 30) (12, 12) (30, 30) (12, 12) (12, 12) (12, 12) (12, 12) (12, 12)

(68, 25) (64, 64) (30, 30) (68, 25) (40, 40) (68, 25) (30, 30) (64, 64) (64, 64)

Before the implementation of a neural network vibration control, some structural analyses were made for further understanding of the behavior of the system. The plates are excited by PZT at resonance frequencies, and utilize PCB352C22 accelerometers for sensing by placing equidistantly along the surface of the plate that has been divided into one hundred points. We obtain 100-points measurements data of mode shape from spectrum analyzer. The data are analyzed by MEscopeVES software [24]. MEscopeVES is a professional software package for analysis of oscillations as well as for dynamic behavior of modal analysis and structural analysis. Through this dynamic analysis of the mode shapes and comparison in theoretical calculations, we can know well the property of vibration plates more. 3.1. Determine the position of excite points and control points Based on dynamic analysis of the mode shapes and several trials and errors by following Lin’s study [25], the best position of exciter to generate the strongest excitation for three different plates are (7.5 cm, 7.5 cm), (21 cm, 21 cm), and (20 cm, 20 cm), respectively. Shown in Table 1. Again in similar manner, the optimum positions for single point controller to reach the best control on acoustic radiation are of little frequency dependence. Therefore, for the smallest plate over full frequency range of interest, a fixed control point at (24 cm, 25 cm) is chosen. Moreover for mid-size plate, the optimum control points at (11.5 cm, 11.5 cm) at either lower or higher modal frequencies, and at either (21 cm, 21 cm) or (48 cm, 48 cm) at mediate modal frequencies are chosen, respectively. As regards to the largest plate, the optimum control points at (30 cm, 30 cm) at lower modal frequencies, at (40 cm, 40 cm) at mediate modal frequency, and at (12 cm, 12 cm) at higher modal frequency are chosen, respectively. The positions mentioned above are manipulated by single frequency as well as double frequency. Additionally, to get better control effectiveness for single frequency, double-point controllers are used as well in this study. Because of too dispersive spreading of the corresponding optimum control points, it is really difficult to describe the details involved and is not discussed here.

K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377

Anechoic chamber

371

1. He-Ne laser 2. Object lens (f=62.9mm)

Plat e

Displacement

3. Photo detector 4. Optical Breadboard

1

Incident path

2

Reflection path

3 4

Fig. 4. Optical system components.

3.2. Optics error signal experimental configuration The side view of the optical sensor apparatus configuration for the experiment is shown in Fig. 4. An optical breadboard is installed in front of an anechoic chamber. The light source of the optical component is a He–Ne laser of diameter 0.68 mm, which has optical wavelength of 632.8 nm. A convex object lens of focal length 62.9 mm is adopted to focus the reflected light beam on the photodetector, which is silicon photodiode (DET-210) and has spectral response from 200 to 1100 nm. Furthermore, as shown in Figs. 5–7, these laser illuminated positions which refer to the MEscopeVES software modal analysis, also carry out the several trials and errors, we can know well the positions in the maximum amplitude of vibration plates. The optimum positions of optics error signal are close to the excited source, the positions of laser beam illuminate for three plates which are (5 cm, 5 cm), (17 cm, 17 cm) and (16 cm, 16 cm), respectively. 3.3. Set up of active control system Fig. 8 shows the set up of all equipments involved in the active control experiment for this study. First of all, through the dynamic experiment for the three plates

involved, we can obtain their natural frequencies. Further, a HP-3245 function generator is used to produce a single frequency signal of various phases and amplitudes, which are divided into two branches through a T-type junction. One of two is taken as the reference input of the neutral network, and the other one is amplified by the TERK Model 601C type power amplifier to excite PZT actuators. The maximum input voltage of HP-3245 function generator is 350 V, and the lowest frequency to be produced by it is 100 Hz. Since the natural frequencies of the first modes for all three plates, and the natural frequency for the second mode of the largest plate are all lower than 100 Hz, the plate modes to be selected for the experiment in this study start with the second modes for the two smaller plates, and starts with the third mode for the biggest plate. The optical error signal received at photo detector is amplified by using a B&K 2633 pre-amplifier. After filtered through a low pass filter, the optical error signal as described is transferred through an A/D converter to a DSP controller. Speaking to the procedures as described, the optical error-path must be modified in real time and appropriately adjust a set of weighting parameters to minimize the dispersion between the desired output and plant response. When making the experiment in progress we can change the dynamical response of vibration plate to

Fig. 5. Illuminate position at (5 cm, 5 cm) by MEscopeVES analysis and theoretical analysis (30*30 cm).

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Fig. 6. Illuminate position at (17 cm, 17 cm) by MEscopeVES analysis and theoretical analysis (60*60 cm).

Fig. 7. Illuminate position at (16 cm, 16 cm) by MEscopeVES analysis and theoretical analysis (86*86 cm).

Fig. 8. Block diagram for the experiment setup of all equipments.

greatly reduce the sound power radiation from its surface. Meanwhile for the sound power measurement, we use the connection of a B&K 3548 sound intensity probe with a B&K 2035 two channel spectrum analyzer to measure the sound intensity radiating from plate surface. 4. Results and discussion The exciter operates by single frequency, and the maximum contributions of radiation are odd–odd modes which

includes (1, 3), (1, 5) and (3, 3). Single control point effect is better than double control point, especially the (3, 3) mode, as shown in Tables 2–4 and the sound intensity spectrum shown in Figs. 9–14, respectively. When it is in 30 cm plate, can reduce 26.1 dB, and 17.1 dB in 86 cm plate. On the contrary, the fewer radiation contribution, such as (2, 2) mode, can reduce 18.3 dB in 30 cm and 10.1 dB in 86 cm, respectively. Table 5 shows that attenuation of residual acoustic power at double frequencies of three plates. From the

K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377

373

Table 2 The residual sound intensity of 30 cm plate before and after control Mode

Frequency (Hz)

Before control (dB)

(1, 1) (1, 2) (2, 2) (1, 3) (2, 3) (1, 4) (3, 3) (2, 4)

95 188 299 348 436 554 594 643

Not excite 74.3 80.5 98.4 82.8 80.3 92.4 87.4

After control (dB) Signal

Residual

%

Double

Residual

%

57.4 62.2 82.6 71.6 67.1 66.3 78.7

16.9 18.3 15.8 11.2 13.2 26.1 8.7

23 23 16 14 16 28 10

66.7 66 78.1 70.9 63.9 66.4 68.2

7.6 14.5 20.3 11.9 16.4 26 19.2

10 18 21 14 20 28 22

Table 3 The residual sound intensity of 60 cm plate before and after control Mode

(1, 1) (1, 2) (2, 2) (1, 3) (2, 3) (1, 4) (3, 3) (2, 4) (3, 4) (1, 5) (2, 5)

Frequency (Hz)

87 138 172 213 256 306 333 357 391 491 533

Before control (dB)

Not excite 71.6 62.1 71.3 63.4 59.8 71.3 56.8 58.2 64.1 67.1

After control (dB) Signal

Residual

%

Double

Residual

%

58.8 45.5 50.7 46.3 41.8 50.5 41.7 41.1 44.7 51.6

12.8 16.6 20.6 17.1 18 20.8 15.1 17.1 19.4 15.5

18 27 29 27 30 29 27 29 30 23

59.3 48.4 51.5 48.5 43.2 51.9 40.9 42.3 40.5 51.1

12.3 13.7 19.8 14.9 16.6 19.4 15.9 15.9 23.6 16

17 22 28 24 28 27 28 27 37 24

Table 4 The residual sound intensity of 86 cm plate before and after control Mode

(1, 1) (1, 2) (2, 2) (1, 3) (2, 3) (1, 4) (3, 3) (2, 4) (3, 4) (1, 5) (2, 5)

Frequency (Hz)

50 84 101 149 199 249 299 349 400 441 528

Before control (dB)

Not excite Not excite 54.9 61.1 70.8 66.7 62.8 64.8 63.2 67.9 68.3

After control (dB) Signal

Residual

%

Double

Residual

%

44.8 41.8 54.1 52.7 45.7 50.1 45.7 57.2 46

10.1 19.3 16.7 14 17.1 14.7 17.5 10.7 22.3

18 32 24 21 27 23 28 16 33

44.4 44.9 52.6 41.9 49.2 52.6 45.4 51.6 50.2

10.5 16.2 18.2 24.8 13.6 12.2 17.8 16.3 18.1

19 27 26 37 22 19 28 24 27

results measured in experiment for single frequency, the excite frequencies chosen effectively in odd–odd mode are composed of (1, 3) and (2, 3), (1, 3) and (3, 3), (3, 3) and (3, 4), respectively. The single controller positions are similar to single frequency. The obtained result as shown in Fig. 15, in the 60 cm plate which is composed of (3, 3) and (3, 4), the acoustic power is more effective about 14.6 dB. All the three plates are given the forms of (1, 3) and (3, 3). The best one in the ranking of sound reduction is the plate of 86 cm, which reduces 9.2 dB, the second one is the 60 cm, and the last one is the 30 cm.

The big area of plate vibrating at higher resonant frequencies, using the double control point is better than using the single point. The vibration modes at higher resonant frequencies are complex and distributes widely. One PZT controller cannot repress all range but local vibration. Therefore, applying two PZT not only repress main sound radiation but also restrain others superimposition mode at high frequency. Controller and error point position are related to controllable efficiency and system stability. Only assigned to a suitable position, we can effectively control the vibration plate. As described below:

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K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377 100

Sound Intensity (dB)

92.4

Before control After control

90 80 70

66.3

60 50 41

40 30 20 10 0 300

350

400

450

500

550

600

650

700

750

800

Frequency (HZ) Fig. 9. Sound intensity at (3, 3) mode 594 Hz by single controller (30 cm).

100

Sound Intensity (dB)

92.4

Before control After control

90 80 70

66.4

60 50 41

40 30 20 10 0 300

350

400

450

500

550

600

650

700

750

800

Frequency (HZ) Fig. 10. Sound intensity at (3, 3) mode 594 Hz by double controller (30 cm).

80 Before control After control

Sound Intensity (dB)

70

71.3

60 50.5

50 40 30 20

15.9

10 0 100

150

200

250

300

350

400

450

500

550

Frequency (HZ) Fig. 11. Sound intensity at (3, 3) mode 333 Hz by single controller (60 cm).

600

K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377

375

80 Before control After control

Sound Intensity (dB)

70

71.3

60 51.9

50 40 30 24 22

20 10 0 100

150

200

250

300

350

400

450

500

550

600

Frequency (HZ)

Fig. 12. Sound intensity at (3, 3) mode 333 Hz by double controller (60 cm).

70 Before control After control

Sound Intensity (dB)

60

62.8

50 45.7 40 30 20 10 0 100

150

200

250

300

350

400

450

500

Frequency (HZ) Fig. 13. Sound intensity at (3, 3) mode 299 Hz by signal controller (86 cm).

70 Before control After control

Sound Intensity (dB)

60

62.8

50

49.2

40 30 20 10 0 100

150

200

250

300 350 Frequency (HZ)

400

450

Fig. 14. Sound intensity at (3, 3) mode 299 Hz by double controller (86 cm).

500

376

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Table 5 The residual sound intensity of double-frequencies before and after control Plate type (cm)

Mode

Frequency (Hz)

Before control (dB) SIL

Total SLI

SIL

Total SLI

30*30

(1, 3) (2, 3) (1, 3) (3, 3)

348 436 348 594

58.6 58.7 66.7 63.5

61.7

45.4 47.7 62.5 52.5

(1, 3) (3, 3) (1, 3) (2, 3) (3, 3) (3, 4)

213 333 213 256 333 391

67.5 66.5 66.6 63.9 64.6 70.2

70.0

(1, 3) (3, 3) (3, 3) (3, 4)

149 299 299 400

56.3 53.7 61 58.6

58.2

60*60

86*86

After control (dB)

68.4

68.5 71.3

63.0

Residual

%

49.7

11.9

19%

62.9

5.5

8%

63.5 51.7 59 59.5 43.3 56.5

63.8

6.3

9%

62.3

6.2

9%

56.7

14.6

20%

47.4 43.9 47.8 52.7

49.0

9.2

16%

53.9

9.1

14%

80 Before control After control

Sound Intensity (dB)

70

70.2 64.6

60

56.5

50 43.3

40 30 20 10 0

0

50

100

150

200

250

300

350

400

450

500

Frequency (HZ)

Fig. 15. Sound intensity are composed of (3, 3)and (3, 4) by double frequencies (60 cm).

(a) Error point position of photo sensor should select the one which approaches to the excite source. (b) If the structure area is smaller; the control point can select the one which works to most modes, that is, to select the one at diagonal 4/5. (c) To the bigger area of plate, the best position of single control point is the one near the excite source at diagonal or the amplitude peak of (3, 3) mode. On the other hand, the best position of the double point at high frequency is at the amplitude peak of (1, 5) mode or at (2, 5) mode that are also located at diagonal.

5. Conclusions An investigation into the optics system take the error signal of vibration surface and modified weighting coefficient, its associated with error back-propagation algorithm of neuron network. Using the control system as described

to reduce acoustic power radiation of vibrating plate is presented in this study. It is very obviously to reveal that using the photo sensor as the source of error signal technique can, whether they are lower or higher resonant frequencies effectively reduce the acoustic power which is radiated from differential areas of vibrating plates. The higher frequencies show an apparently effect. The reason is that the acoustic pressure signal measured at error microphone is an incomplete direct acoustic pressure, which cannot indicate the actual error amount. However, laser is not influenced by sound pressure, so the optical sensor efficiency is superior to the microphone in far field. From the result as measured in experiment for single control point effect in the sound radiation control of plates in lower frequency is superior to that in the double control point. The vibration mode at lower resonant frequencies is pure and has bigger radiation energy, so we only need to repress the main vibrating mode as (1, 2) mode; consequently, the sound radiation decreased considerably. On

K.T. Chen et al. / Applied Acoustics 69 (2008) 367–377

the contrary, using the two PZT controllers causes the raise of unnecessary sound radiate contribution. Besides, the big area of plate vibrating at higher resonant frequencies, using the double control point is better than using the single point. The vibration modes at higher resonant frequencies are complex and distributes widely. One PZT controller cannot repress all range but local vibration. Therefore, applying two PZT not only repress main sound radiation but also restrain others superimposition mode at high frequency. Regarding to the controller and error point position are related to controllable efficiency and system stability. Only assigned to a suitable position, we can effectively control the vibration plates.

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