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Characterization of the Electromechanical Admittance Signatures of Piezo-Impedance Transducers based on its Location
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 18 (2019) 4398–4407
www.materialstoday.com/proceedings
ICMPC-2019
Characterization of the Electromechanical Admittance Signatures of Piezo-Impedance Transducers based on its Location Akshay S. K. Naidu Associate Professor, Department of Civil Engineering, Methodist College of Engineering and Technology (Osmania University), Abids, Hyderabad 500001 INDIA
Abstract The Electromechanical Impedance method (EMI), using piezoelectric ceramics transducers such as Lead-Zirconate-Titanate (PZT), has applications in the fields of non-destructive evaluation (NDE) and structural health monitoring (SHM). The piezoceramic transducer chip (PZT) serves as an actuator supplying vibrational energy when it is bonded to the structure and subjected to harmonic voltage at ultrasonic frequency ranges. The electrical admittance of the PZT is known to be dependent on the dynamic coupling of the mechanical impedances of the PZT and the host structure. The admittance signature obtained over a frequency range serves as a diagnostic signal to monitor structural health. Any defect or damage changes the structure’s mechanical impedance which gets reflected in the admittance signature. This paper examines the changes in the admittance signatures of the same PZT transducer when it is bonded at different locations of a thin plate with cantilever type end conditions. The study is purely numerical using the coupled-field FE simulations in ANSYSTM, yet it gives better insight into admittance signature analysis, which is essential to assessing the structural health.
© 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Piezoelectric transducer chip; Lead-Zirconate-Titanante (PZT), Electromechanical Impedance (EMI) technique; Structural Health Monitoring (SHM); Coupled-field FE analysis
1. Introduction A piezoelectric material undergoes in-plane expansion or contraction upon application of an electrical potential across its electrodes, producing a field that is perpendicular to the plane of deformation. Conversely, application of mechanical strain in a plane perpendicular to the direction of polarization produces electric charge/voltage across its electrodes. The first effect has paved a way for the piezoelectric materials being applied as actuators, while the converse effect lead to applications as sensors [1]. * Corresponding author. Tel.: +91 9959852225 E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019
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The expansion and contraction, in other words, the reversing mechanical strain, can occur alternately at very high rate depending on the frequency of the alternating voltage applied across its electrodes. Typically, piezoelectric ceramics like Lead-Zirconate Titanate (PZT), have the ability to vibrate at ultrasonic frequencies up to the order of mega-hertz, without losing its stability [2] . This property of the PZT has been exploited amply in various applications [3]–[5]. The electromechanical impedance (EMI) method for Structural Health Monitoring (SHM) utilizes the PZT as both actuator and sensor [6], [7]. The PZT is bonded onto the surface of or embedded within the structure. Application of alternating voltage to such a PZT causes local actuation of the host structure at frequency proportional to the applied voltage frequency. The vibration of the PZT coupled with the host structure modulates current flow in the PZT. The coupling between the dynamic mechanical impedances of both the PZT and the host structure is reflected in the electrical admittance output of the PZT, when measured through an impedance measuring device such as a LCR meter or an Impedance Analyzer. This output over a frequency range is termed as admittance signature, which serves as a diagnostic signal for monitoring the health of the structure. Damage in a structure alters the mass, stiffness and damping properties locally. This, in turn, alters the modal parameters, such as the natural frequency of the system and the mode shapes. These get reflected as changes in the admittance signature. The EMI method has been successfully demonstrated for their potential applications in SHM. Over the analytical model of the EMI, numerical models using the coupled field finite elements have demonstrated to give accurate predictions of the system natural frequencies [8], [9]. In this paper, the finite element (FE) simulations of the EMI technique are carried out to study the effect on the admittance signature generated due to the different locations of the PZT on the structure. This attempt is valuable for signature pattern recognition for the purpose of structural health monitoring. The study presented here is a sequel to the studies carried out earlier by the author and fundamentally utilizes the same FE model [10], [11].
2. Numerical Simulations The study aims at understanding the admittance signature patterns obtained by the same PZT when placed at different locations of the structure. For this purpose, a thin metallic plate of dimensions 300 mm length, 20 mm width and 2 mm thickness is considered. This is constrained at one end to form a cantilever type end conditions. The PZT is chosen to have dimensions of 10 mm x 10 mm x 0.3 mm. The respective locations of the PZT on the structure are presented in Table 1 and are shown in Figure 1. The PZT is bonded symmetrically over the width of the top surface of the thin metallic plate. In this analysis, the thickness of the bonding adhesive layer is ignored and the PZT is assumed to be perfectly bonded to the structure. The material properties of the PZT and the metallic plate are listed in Table 2 and Table 3 respectively. Table 1: Distance of the PZT from the fixed end Simulations Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7
PZT location from the fixed end* 10 mm 50 mm 100 mm 150 mm 200 mm 250 mm 290 mm
* (The distance is measured from fixed end of the beam to the centre of the PZT
)
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Fig. 1. Cantilever Metallic Plate bonded by a PZT (a) 3D view (b) - (h) PZT bonded to the plate at different locations Table 2: Properties of the Piezoceramic (PZT) material
Parameters Density
Compliance
Electric permittivity (Relative values) Piezoelectric strain coefficients Mechanical quality factor Damping ratio (Hysteretic) Dielectric Loss tangent
Symbols Ρ s11= s22 s33 s12 = s21 s13= s31 s23= s32 s44= s55 s66 εT11 εT22 εT33 d31 d32 d33 d24 d15 Qm
Values 7800 15 19 -4.5 -5.7 -5.7 39 49.4 1980 1980 2400 -210 -210 500 580 100
ξPZT = (2Qm)-1
0.005
tan
0.02
Units kg/m3
10-12 m2/N
10-12 C/N
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Table 3: Properties for the Host Structure (Metallic Plate) material
Property Young’s Modulus Density Poisson’s ratio Hysteretic damping ratio
Notation & Value E = 6.89 x 1010 N/m2 ρ = 2600 kg/m3 = 0.3 ξ = 0.0005
The coupled-field modeling of the PZT in ANSYSTM is a complete numerical finite element simulation of the EMI technique. Through this simulation, it has been demonstrated that the admittance signatures akin to those experimentally obtained can be directly by harmonic analysis [9]. The complex electrical admittance signature, which is the ratio of electric current to voltage, expressed as: Y = I / V, where Y is the complex electrical admittance of the PZT, V is the sinusoidal voltage applied and I is the modulated current in the PZT, all being complex terms. When the voltage is taken as 1 volt, the output current directly gives the electrical admittance. In ANSYSTM sinusoidal excitation of 1 volt is applied across the PZT which is bonded to the structure. Through Harmonic Analysis for a chosen frequency range, the reaction component namely charge is obtained, and by differentiating we obtain the current. As voltage is 1V, we directly get current at each frequency step. This gives the admittance signature directly. The same method that has been used in the previous works is used in the present work. As the coupled field FE simulations have shown good match with the experimental results, several simulation studies have been carried out for better understanding of the signatures. The influence of changes in the piezoelectric and geometric properties of the PZT on the conductance (real admittance) and susceptance (imaginary admittance) signatures have been studied. It has been confirmed that susceptance signatures are more sensitive to changes in PZT properties while conductance signatures are more sensitive to structural changes [11]. In this work, the specific objective is to study the changes in the conductance signatures when the location of the PZT is changed. Two features of the results are sought. Firstly, modal analysis is carried out to extract the system natural frequencies for different locations of the PZT patch on the plate as per the cases listed in Table 1 and Figure 1. Secondly, the real admittance signatures for each of the cases are extracted by harmonic analysis. The ANSYSTM element SOLID5 is adopted for modeling the PZT transducer chip and SOLID45 is used to model the metallic plate, while assigning the material properties as given in Tables 2 and 3, respectively. As the EMI method works well in ultrasonic frequencies, the frequency range of 20 – 25 kHz is chosen to extract the admittance signatures. The element size refinement chosen for both the metallic plate and the PZT was 1 mm, hexahedral elements as adopted in previous works [9]–[11].
3. Results and Discussion A) From the Modal analysis conducted for all the 7 cases, the system natural frequencies for the cantilever type plate bonded with the PZT are extracted using Block Lancoz eigen value extraction technique in ANSYSTM. The natural frequencies within the range of 20 – 25 kHz are extracted. The mode numbers associated with these frequencies and the corresponding modes of vibration are identified and listed in Table 4. From Figure 1 it may be noted that the xaxis is taken to be along the length, the y-axis along the width and the z-axis along the thickness of the plate. This will help in understanding the last column of Table 4. It is clearly observed that the natural frequencies of the system are changing with the change in the location of the PZT transducer chip on the beam. However, there is no specific trend of the changes in the frequencies correlating to the PZT location. In general, natural frequencies increase with the increase in stiffness. Now, for each mode of vibration there are nodes (zero displacement points) and anti-nodes (maximum displacement points). Thus, it is understood that if the PZT is located near the anti-nodes in a particular mode of vibration, it adds to the stiffness of the system, and thus increases the natural frequency in comparison to the case where the PZT is located near or on the nodes.
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Table 4: System Natural Frequencies for all cases of PZT location Mode 45 46 47 48 49 50 51
Case 1 20258 21472 21659 21828 22057 23934 23956
Case 2 20261 21302 21669 21838 22067 23976 23983
System Natural Frequencies (KHz) Case 3 Case 4 Case 5 20333 20267 20302 21432 21390 21338 21580 21539 21619 21859 21832 21853 22077 22127 22126 23962 23950 23943 23966 23989 23965
Case 6 20311 21473 21681 21839 22075 23944 23982
Case 7 20345 21307 21646 21908 22142 24012 24058
Type of mode
Motion in plane
Torsional longitudinal Flexure Flexure Torsional Torsional Flexuraal
Yz-plane xy-plane(Lateral) xz- plane yz- plane yz- plane multiple
B) Harmonic Analysis results: The conductance signatures extracted for each of the seven cases of Table 1, in the frequency range 20 – 25 kHz, are presented in Figures 2 to 8. In all of these figures, the frequency corresponding to the peaks are corresponding to the natural frequency of the structural system. First observation that can be made from these charts is that out of the 7 frequencies that exist in the chosen frequency range, only two or three frequency peaks are captured in the conductance signatures.
0.0014
Mode 48 21818 Hz (flexural)
Conductance (S)
0.0012
CONDUCTANCE SIGNATURE CASE 1 (20 ‐ 25 kHz)
Mode 51 23946 Hz (flexural multi‐axis)
0.0010 0.0008 0.0006
Mode 46 21472 Hz (longitudinal)
0.0004 0.0002 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 2: Conductance signature for Case 1 (PZT at 10 mm from fixed end)
A.S.K. Naidu et al./ Materials Today: Proceedings 18 (2019) 4398–4407
CONDUCTANCE SIGNATURE Case 2 (20 ‐ 25 kHz)
0.0015
Mode 51 23982 Hz (flexural multi‐axis)
Conductance (S)
0.0012 0.0009 0.0006
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Mode 48 21838 Hz (flexural)
Mode 46 21302 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 3: Conductance signature for Case 2 (PZT at 50 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 3 (20 ‐ 25 kHz) 0.0018
Conductance (S)
0.0015
Mode 48 21858 Hz (flexural)
0.0012 0.0009
Mode 51 23962Hz (flexural)
Mode 46 21430 Hz (longitudinal)
0.0006 0.0003 0.0000 20000
21000
22000
23000
24000
Frequency (Hz) Figure 4: Conductance signature for Case 3 (PZT at 100 mm from fixed end)
25000
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CONDUCTANCE SIGNATURES CASE 4 (20 ‐ 25 kHz) 0.0018
Mode 51 23988 Hz (Flexure Multi axis)
Conductance (S)
0.0015 0.0012 0.0009 0.0006
Mode 46 21390 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz)
Figure 5: Conductance signature for Case 4 (PZT at 150 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 5 (20 ‐ 25 kHz)
0.0015
Mode 48 21852 Hz (Flexural)
Conductance (S)
0.0012 0.0009 0.0006 0.0003 0.0000 20000
Mode 51 23964 Hz (Flexural multi‐axis)
Mode 46 21338 Hz (longitudinal)
21000
22000
23000
24000
25000
Frequency (Hz) Figure 6: Conductance signature for Case 5 (PZT at 200 mm from fixed end)
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CONDUCTANCE SIGNATURES CASE 6 (20 ‐ 25 kHz) 0.0018
Mode 51 23982 Hz (flexure multi‐axis)
Conductance (S)
0.0015 0.0012
Mode 48 21840 Hz (flexural)
0.0009 0.0006
Mode 46 21472 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 7: Conductance signature for Case 6 (PZT at 250 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 7 (20 ‐ 25 kHz)
0.0015
Conductance (S)
0.0012
Mode 51 24058 Hz (flexural)
Mode 48 21908 Hz (flexural)
0.0009 0.0006
Mode 46 21306 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 8: Conductance signature for Case 7 (PZT at 290 mm from fixed end)
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It is observed from Figures 2 to 8 and Table 4 that the natural frequencies corresponding to the torsional modes are not reflected in the signatures. Further, the frequency corresponding to the flexural mode in the lateral direction that is in xy plane is also not reflected in the signatures. This is because the PZT transducer chip is excited in the plane perpendicular to its thickness, that is, the chip vibrates along the plane of the top surface of the plate on which it is bonded. This is because the polarization is along the thickness of the PZT transducer chip and the electrodes to which voltage is applied is on either side across the thickness. Thus, alternating voltage applied to the electrodes cause the PZT chip to vibrate in expansion contraction mode along the plane parallel to the top surface of the plate. This type of PZT actuation invokes flexural mode of vibration of the beam and a partial longitudinal mode of vibration. Thus, it can be understood that only flexural modes and to some extent longitudinal mode is captured in the conductance signatures in Figures 2 to 8. As the actuation of the PZT transducer chip is not invoking torsional mode of vibration of the metallic plate, the torsional modes are not captured in the conductance signatures. Further, the PZT actuation also does not invoke the flexural vibration mode in the lateral plane, i.e. x-y plane. Therefore, the 47th modal frequency, which relates to flexural vibration in lateral direction, is not captured in any of the conductance signatures in Figures 2 to 8. It is also observed that the peaks associated with longitudinal modes in the conductance signatures are of relatively small amplitude as compared to the flexural modes. This is understood as the consequence of the partially longitudinal mode of vibration actuated by the PZT. Had two PZTs been bonded on top and bottom surface and simultaneously actuated in phase then perhaps the peaks could be of larger amplitude as the longitudinal mode would be better invoked. It may be noted that mode 48 is a pure flexural mode with the beam bending in the x-z plane only. However, mode 51, includes flexural vibration in x-z plane and simultaneous bending in the y-z plane. Thus, in general these two modal frequencies are captured and dominated by large amplitudes in most of the charts in Figures 2 to 8. However, in Case 3 and Case 5, when the PZT is located at 100 mm and 200 mm distance from the fixed end, respectively, the amplitude of the peak corresponding to mode 51 is relatively small. This is apparently due to the PZT’s proximity to the vibration nodes in the mode 51. However, further investigation and studies would be required to fully understand this phenomenon. Another, interesting observation is that in Case 4 in Figure 5, the 48th modal frequency, which is prominent in all other cases, is missing. This is because in Case 4, the PZT is located at 150 mm from the fixed end, which is exactly at the longitudinal centre of the metallic plate. The mid-point corresponds to the vibration node (zero displacement point) in the 48th mode and thus the natural frequency is not captured in the signature. As the conductance signature is the diagnostic signal for structural health monitoring applications, it is critical to understand the physical principles involved in its pattern. Based on the above observations the following conclusions can be drawn. (1) The conductance signatures are not the same for a structure and a PZT chip, rather it is significantly dependent on the location where the PZT is bonded on the structure. (2) The PZT transducer chip is to be located on a structure in such a way that it excites maximum number of system natural frequencies. Thus, the locations of vibration nodes are to be avoided for placing the PZT chip. (3) The frequency range chosen for extracting the conductance signature must be such that it contains maximum number of modal frequencies, which are capable of being excited by the PZT, by the virtue of its location. For plate and thin beams, the frequency range that contains maximum number of flexural vibration modes is most suitable. (4) For diagnosis of structural health, the conductance signatures of the PZT bonded onto the structure are derived at two different instances of time and compared for changes. A single conductance signature alone at an instant of time cannot give any conclusion about the structural health. However, this study is useful for identifying the parameters responsible for the location and amplitudes of peaks in the conductance signatures. 4. Conclusions In this paper, results of numerical simulations of the Electromechanical Impedance (EMI) technique have been presented to understand the influence of the PZT chip’s location of bonding onto the structure on the conductance (real admittance) signatures. The couple-field finite elements were used to model the PZT chip in ANSYSTM and modal and harmonic analyses were carried out to extract the system natural frequencies and the
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admittance signatures, respectively. Some key observations have been made and associated conclusive points have been derived, which will be useful in understanding and analysis of the diagnostic signal, namely conductance signature, in the EMI method for SHM applications. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
1.
S. Bhalla, “A mechanical impedance approach for structural identification, health monitoring and non-destructive evaluation using piezo-impedance transducers.,” PhD Thesis, Nanyang Technological University, Singapore, 2004. C. Liang, F. P. Sun, and C. A. Rogers, “Dynamic output characteristics of piezoelectric actuators,” in 1993 North American Conference on Smart Structures and Materials, 1993, pp. 341–352. V. G. Annamdas and M. A. Radhika, “Electromechanical impedance of piezoelectric transducers for monitoring metallic and nonmetallic structures: A review of wired, wireless and energy-harvesting methods,” J. Intell. Mater. Syst. Struct., vol. 24, no. 9, pp. 1021–1042, 2013. C. H. Keilers Jr and F.-K. Chang, “Identifying delamination in composite beams using built-in piezoelectrics: part I—experiments and analysis,” J. Intell. Mater. Syst. Struct., vol. 6, no. 5, pp. 649–663, 1995. Y. Lu, J. Li, L. Ye, and D. Wang, “Guided waves for damage detection in rebar-reinforced concrete beams,” Constr. Build. Mater., vol. 47, pp. 370–378, 2013. K. K. Tseng and A. S. K. Naidu, “Non-parametric damage detection and characterization using smart piezoceramic material,” Smart Mater. Struct., vol. 11, no. 3, p. 317, 2002. V. G. M. Annamdas and C. K. Soh, “Application of electromechanical impedance technique for engineering structures: review and future issues,” J. Intell. Mater. Syst. Struct., vol. 21, no. 1, pp. 41–59, 2010. Y. Yang, Y. Y. Lim, and C. K. Soh, “Practical issues related to the application of the electromechanical impedance technique in the structural health monitoring of civil structures: II. Numerical verification,” Smart Mater. Struct., vol. 17, no. 3, p. 35009, 2008. Y. Y. Lim and C. K. Soh, “Towards more accurate numerical modeling of impedance based high frequency harmonic vibration,” Smart Mater. Struct., vol. 23, no. 3, p. 35017, 2014. A. S. K. Naidu, “Electromechanical Admittance Signature Analysis of Piezo-ceramic Transducers for NDE,” Mater. Today Proc. Elsevier, vol. 5, no. 9, pp. 19933–19943, 2018. A. S. K. Naidu and Vinay Pittala, “Influence of Piezoelectric Parameters on Admittance Diagnostic Signals for Structural Health Monitoring: A Numerical Study,” Int. J. Mater. Struct. Integr., 2018.
ScienceDirect Materials Today: Proceedings 18 (2019) 4398–4407
www.materialstoday.com/proceedings
ICMPC-2019
Characterization of the Electromechanical Admittance Signatures of Piezo-Impedance Transducers based on its Location Akshay S. K. Naidu Associate Professor, Department of Civil Engineering, Methodist College of Engineering and Technology (Osmania University), Abids, Hyderabad 500001 INDIA
Abstract The Electromechanical Impedance method (EMI), using piezoelectric ceramics transducers such as Lead-Zirconate-Titanate (PZT), has applications in the fields of non-destructive evaluation (NDE) and structural health monitoring (SHM). The piezoceramic transducer chip (PZT) serves as an actuator supplying vibrational energy when it is bonded to the structure and subjected to harmonic voltage at ultrasonic frequency ranges. The electrical admittance of the PZT is known to be dependent on the dynamic coupling of the mechanical impedances of the PZT and the host structure. The admittance signature obtained over a frequency range serves as a diagnostic signal to monitor structural health. Any defect or damage changes the structure’s mechanical impedance which gets reflected in the admittance signature. This paper examines the changes in the admittance signatures of the same PZT transducer when it is bonded at different locations of a thin plate with cantilever type end conditions. The study is purely numerical using the coupled-field FE simulations in ANSYSTM, yet it gives better insight into admittance signature analysis, which is essential to assessing the structural health.
© 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Piezoelectric transducer chip; Lead-Zirconate-Titanante (PZT), Electromechanical Impedance (EMI) technique; Structural Health Monitoring (SHM); Coupled-field FE analysis
1. Introduction A piezoelectric material undergoes in-plane expansion or contraction upon application of an electrical potential across its electrodes, producing a field that is perpendicular to the plane of deformation. Conversely, application of mechanical strain in a plane perpendicular to the direction of polarization produces electric charge/voltage across its electrodes. The first effect has paved a way for the piezoelectric materials being applied as actuators, while the converse effect lead to applications as sensors [1]. * Corresponding author. Tel.: +91 9959852225 E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019
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The expansion and contraction, in other words, the reversing mechanical strain, can occur alternately at very high rate depending on the frequency of the alternating voltage applied across its electrodes. Typically, piezoelectric ceramics like Lead-Zirconate Titanate (PZT), have the ability to vibrate at ultrasonic frequencies up to the order of mega-hertz, without losing its stability [2] . This property of the PZT has been exploited amply in various applications [3]–[5]. The electromechanical impedance (EMI) method for Structural Health Monitoring (SHM) utilizes the PZT as both actuator and sensor [6], [7]. The PZT is bonded onto the surface of or embedded within the structure. Application of alternating voltage to such a PZT causes local actuation of the host structure at frequency proportional to the applied voltage frequency. The vibration of the PZT coupled with the host structure modulates current flow in the PZT. The coupling between the dynamic mechanical impedances of both the PZT and the host structure is reflected in the electrical admittance output of the PZT, when measured through an impedance measuring device such as a LCR meter or an Impedance Analyzer. This output over a frequency range is termed as admittance signature, which serves as a diagnostic signal for monitoring the health of the structure. Damage in a structure alters the mass, stiffness and damping properties locally. This, in turn, alters the modal parameters, such as the natural frequency of the system and the mode shapes. These get reflected as changes in the admittance signature. The EMI method has been successfully demonstrated for their potential applications in SHM. Over the analytical model of the EMI, numerical models using the coupled field finite elements have demonstrated to give accurate predictions of the system natural frequencies [8], [9]. In this paper, the finite element (FE) simulations of the EMI technique are carried out to study the effect on the admittance signature generated due to the different locations of the PZT on the structure. This attempt is valuable for signature pattern recognition for the purpose of structural health monitoring. The study presented here is a sequel to the studies carried out earlier by the author and fundamentally utilizes the same FE model [10], [11].
2. Numerical Simulations The study aims at understanding the admittance signature patterns obtained by the same PZT when placed at different locations of the structure. For this purpose, a thin metallic plate of dimensions 300 mm length, 20 mm width and 2 mm thickness is considered. This is constrained at one end to form a cantilever type end conditions. The PZT is chosen to have dimensions of 10 mm x 10 mm x 0.3 mm. The respective locations of the PZT on the structure are presented in Table 1 and are shown in Figure 1. The PZT is bonded symmetrically over the width of the top surface of the thin metallic plate. In this analysis, the thickness of the bonding adhesive layer is ignored and the PZT is assumed to be perfectly bonded to the structure. The material properties of the PZT and the metallic plate are listed in Table 2 and Table 3 respectively. Table 1: Distance of the PZT from the fixed end Simulations Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7
PZT location from the fixed end* 10 mm 50 mm 100 mm 150 mm 200 mm 250 mm 290 mm
* (The distance is measured from fixed end of the beam to the centre of the PZT
)
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Fig. 1. Cantilever Metallic Plate bonded by a PZT (a) 3D view (b) - (h) PZT bonded to the plate at different locations Table 2: Properties of the Piezoceramic (PZT) material
Parameters Density
Compliance
Electric permittivity (Relative values) Piezoelectric strain coefficients Mechanical quality factor Damping ratio (Hysteretic) Dielectric Loss tangent
Symbols Ρ s11= s22 s33 s12 = s21 s13= s31 s23= s32 s44= s55 s66 εT11 εT22 εT33 d31 d32 d33 d24 d15 Qm
Values 7800 15 19 -4.5 -5.7 -5.7 39 49.4 1980 1980 2400 -210 -210 500 580 100
ξPZT = (2Qm)-1
0.005
tan
0.02
Units kg/m3
10-12 m2/N
10-12 C/N
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Table 3: Properties for the Host Structure (Metallic Plate) material
Property Young’s Modulus Density Poisson’s ratio Hysteretic damping ratio
Notation & Value E = 6.89 x 1010 N/m2 ρ = 2600 kg/m3 = 0.3 ξ = 0.0005
The coupled-field modeling of the PZT in ANSYSTM is a complete numerical finite element simulation of the EMI technique. Through this simulation, it has been demonstrated that the admittance signatures akin to those experimentally obtained can be directly by harmonic analysis [9]. The complex electrical admittance signature, which is the ratio of electric current to voltage, expressed as: Y = I / V, where Y is the complex electrical admittance of the PZT, V is the sinusoidal voltage applied and I is the modulated current in the PZT, all being complex terms. When the voltage is taken as 1 volt, the output current directly gives the electrical admittance. In ANSYSTM sinusoidal excitation of 1 volt is applied across the PZT which is bonded to the structure. Through Harmonic Analysis for a chosen frequency range, the reaction component namely charge is obtained, and by differentiating we obtain the current. As voltage is 1V, we directly get current at each frequency step. This gives the admittance signature directly. The same method that has been used in the previous works is used in the present work. As the coupled field FE simulations have shown good match with the experimental results, several simulation studies have been carried out for better understanding of the signatures. The influence of changes in the piezoelectric and geometric properties of the PZT on the conductance (real admittance) and susceptance (imaginary admittance) signatures have been studied. It has been confirmed that susceptance signatures are more sensitive to changes in PZT properties while conductance signatures are more sensitive to structural changes [11]. In this work, the specific objective is to study the changes in the conductance signatures when the location of the PZT is changed. Two features of the results are sought. Firstly, modal analysis is carried out to extract the system natural frequencies for different locations of the PZT patch on the plate as per the cases listed in Table 1 and Figure 1. Secondly, the real admittance signatures for each of the cases are extracted by harmonic analysis. The ANSYSTM element SOLID5 is adopted for modeling the PZT transducer chip and SOLID45 is used to model the metallic plate, while assigning the material properties as given in Tables 2 and 3, respectively. As the EMI method works well in ultrasonic frequencies, the frequency range of 20 – 25 kHz is chosen to extract the admittance signatures. The element size refinement chosen for both the metallic plate and the PZT was 1 mm, hexahedral elements as adopted in previous works [9]–[11].
3. Results and Discussion A) From the Modal analysis conducted for all the 7 cases, the system natural frequencies for the cantilever type plate bonded with the PZT are extracted using Block Lancoz eigen value extraction technique in ANSYSTM. The natural frequencies within the range of 20 – 25 kHz are extracted. The mode numbers associated with these frequencies and the corresponding modes of vibration are identified and listed in Table 4. From Figure 1 it may be noted that the xaxis is taken to be along the length, the y-axis along the width and the z-axis along the thickness of the plate. This will help in understanding the last column of Table 4. It is clearly observed that the natural frequencies of the system are changing with the change in the location of the PZT transducer chip on the beam. However, there is no specific trend of the changes in the frequencies correlating to the PZT location. In general, natural frequencies increase with the increase in stiffness. Now, for each mode of vibration there are nodes (zero displacement points) and anti-nodes (maximum displacement points). Thus, it is understood that if the PZT is located near the anti-nodes in a particular mode of vibration, it adds to the stiffness of the system, and thus increases the natural frequency in comparison to the case where the PZT is located near or on the nodes.
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Table 4: System Natural Frequencies for all cases of PZT location Mode 45 46 47 48 49 50 51
Case 1 20258 21472 21659 21828 22057 23934 23956
Case 2 20261 21302 21669 21838 22067 23976 23983
System Natural Frequencies (KHz) Case 3 Case 4 Case 5 20333 20267 20302 21432 21390 21338 21580 21539 21619 21859 21832 21853 22077 22127 22126 23962 23950 23943 23966 23989 23965
Case 6 20311 21473 21681 21839 22075 23944 23982
Case 7 20345 21307 21646 21908 22142 24012 24058
Type of mode
Motion in plane
Torsional longitudinal Flexure Flexure Torsional Torsional Flexuraal
Yz-plane xy-plane(Lateral) xz- plane yz- plane yz- plane multiple
B) Harmonic Analysis results: The conductance signatures extracted for each of the seven cases of Table 1, in the frequency range 20 – 25 kHz, are presented in Figures 2 to 8. In all of these figures, the frequency corresponding to the peaks are corresponding to the natural frequency of the structural system. First observation that can be made from these charts is that out of the 7 frequencies that exist in the chosen frequency range, only two or three frequency peaks are captured in the conductance signatures.
0.0014
Mode 48 21818 Hz (flexural)
Conductance (S)
0.0012
CONDUCTANCE SIGNATURE CASE 1 (20 ‐ 25 kHz)
Mode 51 23946 Hz (flexural multi‐axis)
0.0010 0.0008 0.0006
Mode 46 21472 Hz (longitudinal)
0.0004 0.0002 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 2: Conductance signature for Case 1 (PZT at 10 mm from fixed end)
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CONDUCTANCE SIGNATURE Case 2 (20 ‐ 25 kHz)
0.0015
Mode 51 23982 Hz (flexural multi‐axis)
Conductance (S)
0.0012 0.0009 0.0006
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Mode 48 21838 Hz (flexural)
Mode 46 21302 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 3: Conductance signature for Case 2 (PZT at 50 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 3 (20 ‐ 25 kHz) 0.0018
Conductance (S)
0.0015
Mode 48 21858 Hz (flexural)
0.0012 0.0009
Mode 51 23962Hz (flexural)
Mode 46 21430 Hz (longitudinal)
0.0006 0.0003 0.0000 20000
21000
22000
23000
24000
Frequency (Hz) Figure 4: Conductance signature for Case 3 (PZT at 100 mm from fixed end)
25000
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CONDUCTANCE SIGNATURES CASE 4 (20 ‐ 25 kHz) 0.0018
Mode 51 23988 Hz (Flexure Multi axis)
Conductance (S)
0.0015 0.0012 0.0009 0.0006
Mode 46 21390 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz)
Figure 5: Conductance signature for Case 4 (PZT at 150 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 5 (20 ‐ 25 kHz)
0.0015
Mode 48 21852 Hz (Flexural)
Conductance (S)
0.0012 0.0009 0.0006 0.0003 0.0000 20000
Mode 51 23964 Hz (Flexural multi‐axis)
Mode 46 21338 Hz (longitudinal)
21000
22000
23000
24000
25000
Frequency (Hz) Figure 6: Conductance signature for Case 5 (PZT at 200 mm from fixed end)
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CONDUCTANCE SIGNATURES CASE 6 (20 ‐ 25 kHz) 0.0018
Mode 51 23982 Hz (flexure multi‐axis)
Conductance (S)
0.0015 0.0012
Mode 48 21840 Hz (flexural)
0.0009 0.0006
Mode 46 21472 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 7: Conductance signature for Case 6 (PZT at 250 mm from fixed end)
CONDUCTANCE SIGNATURES CASE 7 (20 ‐ 25 kHz)
0.0015
Conductance (S)
0.0012
Mode 51 24058 Hz (flexural)
Mode 48 21908 Hz (flexural)
0.0009 0.0006
Mode 46 21306 Hz (longitudinal)
0.0003 0.0000 20000
21000
22000
23000
24000
25000
Frequency (Hz) Figure 8: Conductance signature for Case 7 (PZT at 290 mm from fixed end)
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It is observed from Figures 2 to 8 and Table 4 that the natural frequencies corresponding to the torsional modes are not reflected in the signatures. Further, the frequency corresponding to the flexural mode in the lateral direction that is in xy plane is also not reflected in the signatures. This is because the PZT transducer chip is excited in the plane perpendicular to its thickness, that is, the chip vibrates along the plane of the top surface of the plate on which it is bonded. This is because the polarization is along the thickness of the PZT transducer chip and the electrodes to which voltage is applied is on either side across the thickness. Thus, alternating voltage applied to the electrodes cause the PZT chip to vibrate in expansion contraction mode along the plane parallel to the top surface of the plate. This type of PZT actuation invokes flexural mode of vibration of the beam and a partial longitudinal mode of vibration. Thus, it can be understood that only flexural modes and to some extent longitudinal mode is captured in the conductance signatures in Figures 2 to 8. As the actuation of the PZT transducer chip is not invoking torsional mode of vibration of the metallic plate, the torsional modes are not captured in the conductance signatures. Further, the PZT actuation also does not invoke the flexural vibration mode in the lateral plane, i.e. x-y plane. Therefore, the 47th modal frequency, which relates to flexural vibration in lateral direction, is not captured in any of the conductance signatures in Figures 2 to 8. It is also observed that the peaks associated with longitudinal modes in the conductance signatures are of relatively small amplitude as compared to the flexural modes. This is understood as the consequence of the partially longitudinal mode of vibration actuated by the PZT. Had two PZTs been bonded on top and bottom surface and simultaneously actuated in phase then perhaps the peaks could be of larger amplitude as the longitudinal mode would be better invoked. It may be noted that mode 48 is a pure flexural mode with the beam bending in the x-z plane only. However, mode 51, includes flexural vibration in x-z plane and simultaneous bending in the y-z plane. Thus, in general these two modal frequencies are captured and dominated by large amplitudes in most of the charts in Figures 2 to 8. However, in Case 3 and Case 5, when the PZT is located at 100 mm and 200 mm distance from the fixed end, respectively, the amplitude of the peak corresponding to mode 51 is relatively small. This is apparently due to the PZT’s proximity to the vibration nodes in the mode 51. However, further investigation and studies would be required to fully understand this phenomenon. Another, interesting observation is that in Case 4 in Figure 5, the 48th modal frequency, which is prominent in all other cases, is missing. This is because in Case 4, the PZT is located at 150 mm from the fixed end, which is exactly at the longitudinal centre of the metallic plate. The mid-point corresponds to the vibration node (zero displacement point) in the 48th mode and thus the natural frequency is not captured in the signature. As the conductance signature is the diagnostic signal for structural health monitoring applications, it is critical to understand the physical principles involved in its pattern. Based on the above observations the following conclusions can be drawn. (1) The conductance signatures are not the same for a structure and a PZT chip, rather it is significantly dependent on the location where the PZT is bonded on the structure. (2) The PZT transducer chip is to be located on a structure in such a way that it excites maximum number of system natural frequencies. Thus, the locations of vibration nodes are to be avoided for placing the PZT chip. (3) The frequency range chosen for extracting the conductance signature must be such that it contains maximum number of modal frequencies, which are capable of being excited by the PZT, by the virtue of its location. For plate and thin beams, the frequency range that contains maximum number of flexural vibration modes is most suitable. (4) For diagnosis of structural health, the conductance signatures of the PZT bonded onto the structure are derived at two different instances of time and compared for changes. A single conductance signature alone at an instant of time cannot give any conclusion about the structural health. However, this study is useful for identifying the parameters responsible for the location and amplitudes of peaks in the conductance signatures. 4. Conclusions In this paper, results of numerical simulations of the Electromechanical Impedance (EMI) technique have been presented to understand the influence of the PZT chip’s location of bonding onto the structure on the conductance (real admittance) signatures. The couple-field finite elements were used to model the PZT chip in ANSYSTM and modal and harmonic analyses were carried out to extract the system natural frequencies and the
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admittance signatures, respectively. Some key observations have been made and associated conclusive points have been derived, which will be useful in understanding and analysis of the diagnostic signal, namely conductance signature, in the EMI method for SHM applications. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
1.
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