choice of optimal location of piezoelectric sensor on steel plate … · 2017. 7. 30. · key...

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp. 1225–1230, Article ID: IJMET_08_07_132

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=7

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

CHOICE OF OPTIMAL LOCATION OF

PIEZOELECTRIC SENSOR ON STEEL PLATE

USING MODE SHAPES

Tharun K. Boya

Research Scholar, Department of Mechanical Engineering,

Lovely Professional University, Phagwara, Punjab, India.

Ashok K. Bagha

Assistant Professor, Department of Mechanical Engineering,

Lovely Professional University, Phagwara, Punjab, India.

ABSTRACT

In this paper, the optimal location of the piezoelectric sensor is find out by viewing

the mode shapes of the flexible steel plate. The steel plate is modeled in ABAQUS

software. Then the modal analysis of the flexible steel plate is obtained. A method is

proposed for optimum location of piezoelectric patches by viewing the mode shapes of

the plate. Through viewing method, it can be observed that the piezoelectric sensor

cannot be on the nodal line where displacement is zero as it doesn’t provide an effect.

Key words: Mode shapes, optimal location, piezoelectric sensor.

Cite this Article: Tharun K. Boya and Ashok K. Bagha Choice of Optimal Location

of Piezoelectric Sensor on Steel Plate Using Mode Shapes. International Journal of

Mechanical Engineering and Technology, 8(7), 2017, pp. 1225–1230.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=7

1. INTRODUCTION

The control of vibration by using a piezoelectric actuator and sensor had been the topic of

interest of many researchers as it is the major problem in structures like automobile wings,

tennis rackets, knocking sensors, sports, aircraft, railway compartments, ultrasonic structures,

and few more cavities in order to control the vibrations or disturbances produced by a system

[1]. Even though there are lots of techniques for vibration control such as damping system,

remodeling of structure, extra mass adding, adding vibration isolation, high stiffness materials

which are having good damping proportion, vibration absorber, increasing the width or

thickness of plate are not so appropriate to control the vibrations produced i.e. low natural

frequencies. These techniques are failing due to lower frequencies; the wavelength will

increase enormously which leads to the layer thickening of the noise absorbing systems and it

will append the extra weight to the structure, therefore, it gets hard. As many advancements

arrived in modern laptops had found an alternative at lower natural frequencies for this

Tharun K. Boya and Ashok K. Bagha


passive control systems in order to eradicate the unnecessary disturbance or sound. Based on

the natural frequency range, the active and passive control methods are divided as disturbance

below 1000Hz is an active method and if disturbance above 1000Hz is a passive method [2].

But most of the times the active control method is preferred because it has a competency to

operate at antithetical conditions.

The Piezoelectricity means to generate an electric charge. This electricity is formed due to

the pressure that which propagates on materials such as ceramics, solid crystals. The effect

produced by piezo will acts as the relation between electrical and mechanical systems. This

effect is reversible when mechanical force is applied results in the generation of the electrical

field. Similarly, it will act as irreversible when electrical forces are applied results in the

generation of mechanical field [3, 4]

From the literary survey, it is found that if the absence of piezoelectric patch may lead to

deflection and buckling of material due to load. Then in presence of piezoelectric, deflection

and buckling is avoided. Piezoelectric patch is used for vibration control purpose which is

produced in systems because of reliability, easiness and regarding mass added to structures

will not make heavy [5]. But while fixing piezo patch, on the top surface sensor is located and

at the bottom surface, the actuator is located. From sensor, the actual control loop signal will

generate and then this signal is transferred to the actuator. From there actual effect will be

acting on the system to control the vibrations.

For optimization, vibration control, detection of any damages in structures or systems and

better improvement of dynamic characteristics a modal analysis had been a prominent

technology. This modal analysis not only limited to mechanical, automobiles but also

applicable for aircraft structures, buildings, bio-medicals etc., when no external load is acting

on a system, then free vibrations will occur due to oscillations produced by an initial

deflection [6]. Then systems possess some amount of natural frequencies due to stiffness

distribution and mass distribution and degrees of freedom. If it is a continuous system, it will

result in infinite no of degrees of freedom and infinite no of frequencies [7]. In this paper, the

optimal location of the piezoelectric sensor is find out by viewing the mode shapes of the

flexible steel plate. A method is proposed for optimum location of piezoelectric patches by

viewing the mode shapes of the plate.

2. METHODOLOGY

FE model of the steel plate and optimal location of piezoelectric patch: In this section, FEM

of steel plate is carried out.

2.1. Finite element modeling of neat plate

An FE model of the steel plate is made in Abaqus software by considering the length of

0.261m, breadth of 0.3m, and thickness of 0.001m. Properties of steel are taken as Young’s

modulus of E=200 G-Pa, density of ρ=7800Kg/m3, Poisson’s ratio of ν = 0.3. The boundary

condition is taken as clamped at all edges. Mesh size of 10×12 is considered [6]. Finally,

Modal shapes of steel plate are taken out.

2.2. Viewing the mode shapes of neat plate

Mode shapes of the neat plate are shown in [Figure 1, Figure 2, Figure 3, and Figure 4]. In

this section, the optimal location is found out by viewing the modal shapes of the plate. It is

observed that there are nodal lines on the plate where the plate displacement is zero. It is

observed that there is no nodal line in the 1st mode, one horizontal at the center of 2nd mode,

one vertical at the center of 3rd mode, horizontal and vertical at 4th mode. So, it can be

Choice of Optimal Location of Piezoelectric Sensor on Steel Plate Using Mode Shapes


concluded that piezoelectric sensor should not be at the nodal lines. If the sensor will be

placed at the nodal line it will not sense that mode.

2.3. FE model of the plate-piezoelectric patch

A piezo P-876 A12 Dura Act piezoelectric patch is considering by taking a length of

0.0522m, breadth of 0.05m and thickness of 0.0005m. Properties of piezoelectric patch is

taken as Young’s modulus of E=23.3 G-Pa, Density of ρ=7800Kg/m3 Poisson ratio of ν =

0.34, Piezoelectric strain coefficient e31 = -8.9678 C/m2, e32 = -8.9678 C/m2, Dielectric

constant ɛ33 = 6.6075e-9. Mesh size of 2x2 is considered [6]. Finally, Modal shapes of steel

plate with the piezoelectric patch are taken out. In Abaqus software, the piezo patch is

attached to the steel plate by using tie which is taken from constraint option in order to control

the vibrations produced by the plate. Similarly, the job is created and Mode shapes of the

plate-piezoelectric patch are extracted out.

2.4. Optimal location of piezoelectric patch using modal analysis

Best preferable location of the piezoelectric patch is found out in ABAQUS CAE software by

viewing method.

2.4.1. Method: Viewing the mode shapes of neat plate

In this method, the modal analysis is conducting in which mode shapes are extracted out.

With the help of mode shapes, piezoelectric sensor cannot be placed at the nodal line where

displacement is minimum. By viewing the mode shapes of the neat plate, from [Figure 1] it is

observed that in 1st mode shape, no nodal line is formed. From [Figure 2] it is observed out

that in 2nd mode shape, the nodal line is formed horizontally. From [Figure 3] it is observed

that in 3rd mode shape, the nodal line is formed vertically. From [Figure 4] it is observed that

in 4th mode shape, the node line is formed as a quadrant. Piezo cannot be placed at nodal

lines in which displacement is zero and control of vibration also fails. So, by viewing the

modal shapes of the neat plate. Since the rectangular plate is clamped at all edges, it is divided

into four coordinates. By viewing the one of the quarter quadrant is same as remaining three

quadrants.

From Table 1, Initially piezo is placed at center location L1 (61, 62, 72, 73) and viewed

that 1st mode shape is possible as no nodal line is passing through piezo but 2nd mode shape

is not possible as the horizontal nodal line is passing through piezo, then 3rd mode shape is

not possible as the vertical nodal line is passing through piezo, then 4th mode shape is also

not possible as both horizontal and vertical nodal lines are passing through piezo. So, it is

concluded that location L1 is not the optimum location. Then Piezo is placed on the horizontal

line at location L2 (60, 61, 71, 72) and viewed that 1st mode shape is possible but 2nd mode

shape, 3rd mode shape, 4th mode shape is not possible as nodal lines are passing through

piezo. Similarly, Location L2 is not the preferable location.

Then piezo is placed on the vertical line at location L3 (59, 60, 70, 71) and it is found out

that 1st mode shape is possible but the 2nd mode shape, 3rd mode shape, 4th mode shape is

not possible as nodal lines are passing through piezo. Likewise, Location L3 is also not the

optimal location. Finally, piezo is moved to location L4 (37, 38, 48, 49), from [Figure 5] it is

observed that 1st mode shape is possible as no nodal line is passing through piezo. From

[Figure 6], it is observed that 2nd mode shape is possible as no nodal line is formed. From

[Figure 7], it is observed that 3rd mode shape is possible as no nodal line is formed. From

[Figure 8], it is observed that 4th mode shape is possible as no nodal line is formed. So, at

location L4 (37, 38, 48, 49) is the optimum location as no nodal line is passing through the

piezo.



3. SIMULATION RESULTS

FIG I, FIG II, FIG III, and FIG IV, represents the Mode shapes of the neat plate with Natural

Frequency are shown.

Figure 1 1st mode shape frequency 117 Hz Figure 2 2nd mode shape frequency 223 Hz

Figure 3 3rd mode shape frequency 272 Hz Figure 4 4th mode shape frequency 364 Hz

FIG V, FIG VI, FIG VII, and FIG VIII represents the Mode shapes of most preferable

location of piezoelectric patch with Natural frequency are shown.

Figure 5 1st mode shape frequency 117 Hz Figure 6 2nd mode shape frequency 220 Hz

Choice of Optimal Location of Piezoelectric Sensor on Steel Plate Using Mode Shapes


Figure 7 3rd mode shape frequency 269 Hz Figure 8 4th mode shape frequency 354 Hz

Table 1 Presents the different locations of piezoelectric patch on plate

Table 1 Different locations of piezoelectric patch

4. CONCLUSION

In this paper, the choice of optimal location of the piezoelectric sensor on steel plate is

proposed by using the modal analysis. It is concluded that in order to control the vibrations

produced by the system is done by attaching a piezoelectric sensor to the plate. Then mode

shapes of steel plate with piezo are found out by conducting the modal analysis in ABAQUS

software. By viewing the mode shapes of the plate with piezo it is observed that the

piezoelectric sensor cannot be placed on the nodal line where displacement is minimum. Then

this will not provide an effect for controlling the vibrations.

Finally, after placing the piezo at different locations on a steel plate. It is found out that

Location L4 (37, 38, 48, 49) is considered as a best optimum location for the piezoelectric

sensor as it is satisfying all the mode shapes where no nodal lines are passing through the

piezo. This optimum location will control the vibrations which are produced by the system

effects. With the help of the viewing method, it is observed that finding the most optimum

location of piezo is very quick.

5. ACKNOWLEDGEMENT

I feel thankful to IIT Delhi for providing the opportunity to work in Abaqus software and it is

also an immersive pleasure to precede the work.



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