CHOICE OF OPTIMAL LOCATION OF PIEZOELECTRIC SENSOR ON STEEL PLATE USING MODE SHAPES

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp , Article ID: IJMET_08_07_132 Available online at ISSN Print: and ISSN Online: 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 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 editor@iaeme.com

2 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 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 is considered [6]. Finally, Modal shapes of steel plate are taken out 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 editor@iaeme.com

3 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 FE model of the plate-piezoelectric patch A piezo P-876 A12 Dura Act piezoelectric patch is considering by taking a length of m, breadth of 0.05m and thickness of m. 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 = C/m2, e32 = C/m2, Dielectric constant ɛ33 = e-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 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 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 editor@iaeme.com

4 Tharun K. Boya and Ashok K. Bagha 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 1 st mode shape frequency 117 Hz Figure 2 2 nd mode shape frequency 223 Hz Figure 3 3 rd mode shape frequency 272 Hz Figure 4 4 th 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 1 st mode shape frequency 117 Hz Figure 6 2 nd mode shape frequency 220 Hz editor@iaeme.com

5 Choice of Optimal Location of Piezoelectric Sensor on Steel Plate Using Mode Shapes Figure 7 3 rd mode shape frequency 269 Hz Figure 8 4 th 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 editor@iaeme.com

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