3.6 Numerical analysis of the EI response of PZT patch
3.6.1 Modelling PZT-structure Interaction
The PZT-structure interaction was evaluated using a numerical simulation of the EI response of a PZT patch bonded to 40 mm cube. A numerical model of the PZT patch bonded to a concrete cube was developed in COMSOLTM Multiphysics (Fig. 3.10). The epoxy thickness was assumed to be equal to 0.1 mm and its isotropic loss factor was taken as 0.05. The properties of epoxy are given in Table 3.1. The properties of the concrete are taken as in Table 3.1. The isotropic loss factor (đťś‚) of concrete was assumed to be 0.03.
Considering symmetries, a one fourth model of the PZT coupled to concrete cube was developed. Similar to the analysis of the free PZT, the 20 mm x 20 mm faces were treated as equipotential surfaces and a potential of 1 V was applied across the opposite faces of the PZT patch. The frequency of the voltage excitation was varied from 10 kHz to 500 kHz and the analysis was performed with a frequency interval of 613.2 Hz. The updated properties of the PZT given in Table 3.3 were used in the simulation.
Figure 3.10: The finite elem ent (FE) m odel for sim ulating im pedance response of PZT bonded to a cube in COM SOL
PZT
Adhesive Layer
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Figure 3.11a shows a comparison of conductance plot obtained from experiments and numerical simulation. Numerical simulation provides a good prediction of resonance frequencies. While the numerical analysis slightly under predicts the resonance frequencies, there is a large difference in the predicted amplitude. The differences in the magnitudes of the predicted and the experimental resonant peaks values are attributed to several factors such as damping of the substrate and epoxy, the thickness and the stiffness of the epoxy layer. The exact values of damping for the two materials and the stiffness of the epoxy are not known precisely [78].
From simulations, the following were recorded. Changes in the thickness and the stiffness of the epoxy produced changes in the magnitude of the resonant peak accompanied with a frequency shift. The influence of these parameters is more on the frequency content than the magnitude of the peak. An increase in the material damping of epoxy produced a decrease in both the frequency and the amplitude of resonant peak. The influence of damping is more on the amplitude of resonant peak than the resonant frequency. An increase in the substrate damping was found to have a significant influence on decreasing the amplitude of the local peaks present at low frequencies.
The thickness and the elastic modulus of the epoxy layer and the isotropic loss factors of the epoxy and the concrete substrate were changed iteratively to match the experimental response. The final values of the parameters which produced a close match with the experimental result are shown in Table 3.4.
A comparison of the conductance response of the coupled PZT patch calculated using updated properties is shown in Fig. 3.11b. It can be seen that the numerical model with updated values of parameters gives a very good prediction of the electrical conductance response of the PZT patch bonded to a concrete cube.
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Table 3.4: U pdated param eters of the epoxy and concrete substrate used in num erical sim ulation
Parameter Value Updated value
Thickness of epoxy layer 0.1 mm 0.05 mm Loss factor damping of epoxy 0.05 0.02
Loss factor damping of substrate
0.03 0.017
Young’s modulus of the epoxy 2 GPa 4 GPa
(a) (b)
Figure 3.11: Com parison of electrical conductance response of a PZT patch bonded to a 40 m m concrete cube: (a) W ithout correction; (b) W ith updated
m aterial constants
The calibrated model for the coupled EI response of a PZT patch bonded to a 40 mm cube was extended to evaluate the influence of finite size of substrate on the coupled EM response of PZT patches of different size. The responses of 10 mm and 5 mm square PZT patches of 1 mm thickness were evaluated. The updated material parameters, from the previous analysis were used in the numerical simulations. The electrical conductance signatures of the free PZT patches of different sizes are shown in Fig. 3.12a. There are increases in the resonant frequencies of the free PZT patches with a decrease in its size. As a reference, the frequency of the first resonant mode of the 20 mm, the 10 mm and the 5 mm square PZT patches are equal to 84.16 kHz, 168 kHz, and 334.22 kHz, respectively. The coupled EI response of a bonded PZT patch was
1E-08 0.0000001 0.000001 0.00001 0.0001 0.001 0.01
10000 210000 410000
Conductance(S)
Frequency (Hz)
40mm cube_Expt.
40mm cube_Sim.
0.000001 0.00001 0.0001 0.001 0.01
10000 210000 410000
Conductance(S)
Frequency (Hz)
40mm cube_Expt.
40mm cube_Sim.
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evaluated from the electrical conductance measurements over a range of frequencies. The electrical conductance signatures of the PZT patches of different sizes bonded to the 40mm cube are shown in Fig. 3.12b. On decreasing the size of the PZT patch, the resonant peaks identified in the conductance response of the PZT patches bonded to the concrete cube also show an upward shift in the resonant frequencies and the local resonance peaks identified with the structural vibration modes of the finite sized substrate become less prominent. The narrow, closely-spaced peaks are prominently identified over all the broad resonant peaks in the response of the 20 mm PZT patch bonded to the concrete cube. For the 10 mm patch, the closely spaced peaks overlap with the first peak in the electrical conductance spectrum of the bonded PZT patch. The closely spaced structural modes are not evident in the coupled electrical conductance response of the 5 mm PZT patch.
(a) (b)
Figure 3.12: The electrical conductance response of PZT patc hes obtained using the calibrated num erical m odel with updated m aterial properties: (a) Free response of PZT patches of different sizes (b) R esponse of PZT patches of
different sizes bonded to 40 m m concrete cube.