INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Finite Element Analysis for the Design of a Protective Layer of a Disc
Piezoelectric Energy Harvester
Song-Guk Kim, NamChol Yu*
Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of Korea
* Corresponding Author
DOI: https://dx.doi.org/10.51584/IJRIAS.2025.100900098
Received: 16 August 2025; Accepted: 23 August 2025; Published: 25 October 2025
ABSTRACT
In this paper, an energy harvester using piezoelectric is designed and ANSYS simulation results are reported.
The energy harvester was made in the form of a disk. The top and bottom surfaces of the piezoelectric disk
ceramics were made by combining metal shields. The effectiveness of the protective layer was evaluated by
simulating the actual pressure distribution on the piezoelectric when the energy harvester with the protective
layer was subjected to pressures of 0.05, 0.1, 0.3, 0.5, and 1 MPa.
Keywords: energy harvester, ANSYS simulation, disc, piezoelectric ceramics, protective layer
INTRODUCTION
Pb(Zr(1-x)Tix)O3(PZT) has been used for many applications such as sound generation, detection, high
pressure generation, vibrating devices, energy harvesting, etc., due to both static and inverse piezoelectric
effects. In particular, PZT materials have the ability to convert mechanical energy into electrical energy [1-3].
The piezoelectric energy collector can convert small vibrations into electrical energy and has high conversion
efficiency. It also has the advantage of generating electricity in the dark and at night without sunlight. Hence, it
is always possible to generate electricity where vibration, pressure or force is applied [3,4]. To obtain electrical
energy from mechanical vibrations, a piezoelectric plate that does not break even at high external pressures has
to be developed. The most important challenge in designing and developing PZT piezoelectric devices for
energy generation is to have a structure that is not destroyed by the strong mechanical forces applied to the
piezoelectric devices repeatedly.
Since it is important to perform an optimal structural design by performing simulations prior to actual
manufacturing of the device, many researchers have used simulation programs such as ANSYS, MATLAB,
COMSOL, and ABAQUS. ANSYS, one of the finite element analysis programs, is the most effective program
for the analysis of structures, heat, fluids, electromagnetic, stress distributions, acoustic fields and their
coupling problems, and has found wide application in various fields of science and technology [5].
Therefore, we aim to simulate and analyze the stress distribution and voltage evolution in the case of the
copper plate coated with the protective layer of PZT and to design a suitable copper plate protective layer
structure.
Structure and operating principle of piezoelectric energy harvester
The charge generated by pressure changes is not long-lasting and soon disappears, so it is used for the
observation of transient changes. The static pressure effect is a voltage-generating phenomenon, in which the
electric signal is generated by applying an external stress and a vibration displacement to the piezoelectric. It is
applied to a piezoelectric device for ignition, such as a gas igniter. And the reverse piezoelectric effect is a
displacement generation phenomenon, in which the piezoelectric is subjected to external voltage, which causes
mechanical deformation, and is mainly applied to the actuator. The static pressure and the inverse pressure
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Page 996
effects are collectively called piezoelectric effects, and the energy harvesting technique uses static pressure
effects.
Figure 1 is a model of a disk piezoelectric device coated with a protective layer of 0.3 mm thick copper.
Figure. 1. Structure and Principles of Disc Energy Harvesters.
The first one in Fig. 1 is the absence of F on the piezoelectric device, so that the ceramic diameter does not
increase. The second showed that F was applied to the disc plate, and the vertical force F was transferred,
leading to an increase in the ceramic diameter. This force causes the charge to be generated by the polarization
of the lower and upper electrodes by g31. By this construction and principle, electric energy can be collected
by installing piezoelectric elements in the presence of vibrations such as road floors.
Table 1. Characteristic parameters of PZT used in this paper
parameters
notice
value
density
ρ(g/㎤)
7.80
permittivity at constant stress
(polarization direction)
(vertical direction)
ε
33
T
/ε
0
ε
11
T
/ε
0
1450
1400
curie temperature
T
c
(℃)
345
dielectric dissipation factor
tanδ(10
-3
)
20
coupling factor
k
p
k
t
k
31
k
33
0.62
0.48
0.35
0.69
piezoelectric charge coefficient
d
31
, d
32
d
33
d
24
, d
15
-165(×10
-12
C/N)
360(×10
-12
C/N)
497(×10
-12
C/N)
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Page 997
piezoelectric voltage
coefficient
g
31,
g
32
g
33
g
24,
g
15
-12.9(×10
-3
Vm/N)
27(×10
-3
Vm/N)
38.9(×10
-3
Vm/N)
Finite element analysis
Using the finite element analysis software ANSYS 16.0, the piezoelectric energy harvester was simulated to
consider various characteristics and select the optimum size and shape. The elastomer was fixed with a brass
thickness of 0.3 mm, a diameter of 28 mm and a height of 3 mm. Piezoelectric ceramics were used with PZT
with the characteristic values shown in Table 1.
The first simulation analyzed the actual stress distribution in the piezoelectric under 0.05, 0.1, 0.3, 0.5, and 1
MPa of pressure applied to the energy harvester with the protective layer. The piezoelectric thickness was 1
mm and the refraction angle of the copper plate was fixed at 15°. The second simulation simulated the stress
distribution by varying the angle of bending of the protective layer copper plate at 1 mm thickness and applied
pressure of 0.1 MPa at 5°, 15°, and 45°. The third simulation was performed by varying the piezoelectric
thickness to 0.5 mm, 1 mm, 1.5 mm and 2 mm at applied pressure of 0.1 MPa and angle of refraction of the
shield copper plate.
Experimental results and discussion
Fig. 2 shows the results of the stress distribution simulation with the pressure variation applied in the designed
assembly. The piezoelectric thickness was 1 mm and the angle of refraction of the shield was 15°.
Figure. 2. Stress distribution with variation pressure applied in the designed assembly device
(piezoelectric thickness of 1 mm, angle of break of protective copper plate 15°),
(a)-0.05 MPa, (b)-0.1 MPa, (c)-0.3 MPa, (d)-0.5 MPa, (e)-1MPa, (f)-1 MPa
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Page 998
As can be seen, the force applied perpendicular to the piezoelectric element by a copper plate protective layer
with a folded structure was applied by the horizontal decomposition. Also, the force on the indenter increases
with increasing applied pressure, and the vertical force increases above 1 MPa, which results in the
piezoelectric bending. Thus, it is shown that the designed piezoelectric device can be damaged above 1 MPa.
Fig. 3 shows the results of the simulation of stress distribution along the angle of refraction of the shielded
copper plate. The piezoelectric thickness was 1 mm and the applied pressure was 0.1 MPa. The simulation
results showed that the force acting in the horizontal direction decreased as the angle of refraction of the shield
plate increased, while the force acting in the vertical direction became larger and larger. Finally, when the
angle of refraction is 5°, the force acting in the horizontal direction is the largest.
Figure3. Stress distribution along the angle of refraction of protective copper plates in the designed assembly
(piezoelectric thickness of 1 mm, applied pressure of 0.1 MPa), (a)-5°, (b)-15°, (c)-45°
Table 2 shows the results of the power voltage simulation with the variation of the thickness of the
piezoelectric. The angle of refraction of the shield copper plate was 15° and the applied pressure was 0.1 MPa.
The simulation results showed a maximum value of 3.80767 V when the thickness was 0.5 mm and a
minimum value of 2.16208 V when the thickness was 2 mm. That is, the generation voltage tended to decrease
as the thickness of the piezoelectric increased.
The voltage generated in the piezoelectric can be calculated by the following equation:
where d is the piezoelectric coefficient, A is the area of the piezoelectric under the force, F is the force acting
on the piezoelectric, and t is the thickness of the piezoelectric. As can be seen from this equation, the voltage
generated increases as the thickness of the piezoelectric increases.
However, in our proposed piezoelectric device, the power voltage decreases despite the increase in the
thickness of the piezoelectric. This is because the force applied in the vertical direction is decomposed by a
protective copper plate with a folded structure into a horizontal force, and a voltage is generated. The larger the
thickness of the piezoelectric, the larger the area under which the horizontal force is applied, the smaller the
generated voltage. Thus, in the proposed piezoelectric energy harvester, the generated voltage increases with
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Page 999
smaller piezoelectric thickness and larger diameter. However, it is important to take into account the voltage
generation and the breaking strength, since too small a thickness of the piezoelectric can easily break down
even under small forces.
Fig.4. occurrence voltage with varying thickness of piezoelectric in the designed assembly
(15° of protective layer angle, 0.1 MPa of applied pressure), (a)-5°, (b)-15°, (c)-45°
Fig.5. Variation of power voltage with thickness of piezoelectric element
Table 2. Variation of the generated voltage with the thickness of the piezoelectric element
thickness of piezoelectric, mm
occurrence voltage, V
0.5
3.80767
1
3.08963
1.5
2.55097
2
2.16208
3.80767
3.08963
2.55097
2.16208
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5
occurrence Voltage, V
thickness of piezoelectric element, mm
INTERNATIONAL JOURNAL OF RESEARCH AND INNOVATION IN APPLIED SCIENCE (IJRIAS)
ISSN No. 2454-6194 | DOI: 10.51584/IJRIAS |Volume X Issue IX September 2025
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Page 1000
CONCLUSIONS
The protective layer proposed in this paper is a protective action of piezoelectric and a horizontal
decomposition of the vertical force. The generated voltage with the thickness of piezoelectric ceramics
decreases with increasing thickness of ceramics. This is because the piezoelectric device with the proposed
structure generates a voltage by a radial force. Thus, in our designed piezoelectric device, the smaller the
thickness of the piezoelectric, the larger the generated voltage. The generated voltage along the angle of
refraction of the protective copper plate was highest when the angle was 5°. However, the increase in energy
harvester size is a drawback to maintain a constant gap between protective copper plates and piezoelectric
ceramics and to maintain a 5° angle of refraction of protective copper plates. Future work will focus on the
appropriate device structure and protective layer material to achieve optimum angle of refraction of the
protective layer.
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