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Article

Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force

by
Su Xian Long
1,
Shin Yee Khoo
1,2,3,*,
Zhi Chao Ong
1,2,3,
Ming Foong Soong
1 and
Yu-Hsi Huang
4,5
1
Department of Mechanical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
2
Advanced Shock and Vibration Research Group, Applied Vibration Laboratory, Block R, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
3
Centre of Research Industry 4.0 (CRI 4.0), Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
4
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan
5
Graduate School of Advanced Technology, National Taiwan University, Taipei 10617, Taiwan
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(22), 15899; https://doi.org/10.3390/su152215899
Submission received: 29 September 2023 / Revised: 5 November 2023 / Accepted: 10 November 2023 / Published: 13 November 2023
(This article belongs to the Section Energy Sustainability)
Browse Figures
Versions Notes

Abstract

:
In recent years, much research has been carried out to enhance the efficiency of the piezoelectric energy harvester (PEH). This study focuses on the performance of the compressive Hull PEH under impact forces, which simulates real-world scenarios, such as foot strikes or vehicular wheel excitations, more accurately compared to harmonic forces. The experimental results prove the performance of the Hull PEH with less than 5.2% of deviation compared to finite element analysis outcomes under impact forces between 10 N and 1 kN. The Hull PEH more substantially amplified the input force and compressed the piezoelectric material, which was Lead Zirconate Titanate (PZT). Consequently, it amplified the voltage output of a standalone PZT up to 16.9 times under a similar boundary condition. A maximum peak power output of 7.16 W was produced across 50 kΩ of optimum load resistance under 1 kN of impact force, which surpassed the benchmark Cymbal PEH by 37.68 times. Furthermore, it demonstrated a higher energy conversion efficiency of 84.38% under the impact force compared to the harmonic force. This research conclusively proves that the Hull PEH has superior performance in terms of voltage output, power output, loading capacity, and efficiency, making it a promising technology for impact loading applications to generate green energy.

1. Introduction

In line with the global ambition to achieve carbon neutrality and meet the sustainable development goal, the emphasis on green energy technology has intensified over the past several decades [1,2]. This period has witnessed a remarkable surge in the development of renewable energy sources as alternatives to fossil fuels. These renewable energy solutions include solar, wind, hydro, geothermal, and biomass energy, with recent advancements also leveraging the potent energy found in ocean waves and tides [3]. The suitability of these sources is often dictated by specific locational conditions, including factors like the availability of sunlight, wind conditions, and the feasibility of onshore or offshore installations [4].
In this evolving landscape, a promising green technology has emerged, capitalizing on the ability of piezoelectric materials to convert mechanical energy from various vibrational sources into electricity with improved sustainability [5,6]. These sources of vibration can be as diverse as human motions [7], such as foot strikes in shoes [8] or floor tiles [9,10], to vehicular movements on roadways [11,12], railway vibrations [13], and even vibrations from household appliances such as air conditioners [14] or from rotating machines via rolling element bearings [15] and shafts to achieve self-powered sensor networks [16]. Innovatively, some applications have even integrated with fluid flows found in wind [17] or water pipes [18]. This piezoelectric energy harvesting technology stands as a significant asset in powering wireless sensor nodes (WSNs), where power consumption is typically low [19]. Implementing this technology can mitigate the hassles associated with frequent battery replacements and offer a solution for locations that are difficult to access or where other energy sources like solar power are unfeasible [20]. Examples include underground subways or remote, unmanned facilities that have stringent space or accessibility constraints. Additionally, this technology proves invaluable in structural health monitoring, aiding in the real-time assessment and maintenance of infrastructure elements such as buildings and bridges [21].
Consequently, there has been a significant increase in research focused on enhancing the efficiency of piezoelectric energy harvesting. It covers various areas including material composition, innovative mechanisms for more efficient motion conversion, amplifier frame structural designs, the frequency tuning method, and improvements in electronic components such as electrode polarization methods and energy storage solutions. Long [22] summarized the various types of mechanical amplifier structures for the piezoelectric energy harvester (PEH), ranging from the cantilever and flexure to multistage types as shown in Figure 1. The flextensional structures, namely the Cymbal [23,24] and Rhombus [25,26,27], have been widely applied in high-force environments due to their robust structure capable of withstanding high stress. Since the compressive yield strength of piezoelectric materials is ten times higher than their tensile yield strength, Kuang [28] developed a flexcompressive structure integrated with a piezoelectric stack to achieve higher power output.
A compressive Hull PEH has been developed that utilizes the ceramic type of piezoelectric material, Lead Zirconate Titanate (PZT), which is suitable for vehicular excitation [29]. The simulation results show that it can generate a power output of 11.34 mW under a 1 kN sinusoidal force at 2 Hz, thereby surpassing the benchmark Cymbal structure threefold. However, previous research on PEH or Hull PEH has mostly involved harmonic excitations. An impact force can be applied to the Hull PEH to demonstrate applications such as human foot strikes in shoes, floor tiles, and vehicle wheel loading on road surfaces [30,31] (see Figure 2), which is the main focus of this study.
Therefore, in this study, a tensile type of Cymbal amplifier structure PEH, which is optimized by Kuang [32], is selected as a benchmark case. The compressive Hull PEH and the benchmark tensile Cymbal PEH, which utilize PZTs of the same size, are tested under identical impact force conditions to ensure a fair comparison. This study involves the development of a coupled piezoelectric-circuit finite element model (CPC-FEM) using ANSYS™ 18.2 software (ANSYS, Inc., Canonsburg, PA, USA). The findings from the finite element analysis (FEA) are corroborated experimentally, providing a comprehensive evaluation of energy harvesting performances in terms of power output and efficiency under the impact force.

2. Numerical Analysis

In the structural analysis simulation, the Hull and Cymbal PEHs are constructed with the dimensions as presented in Figure 3 and Table 1. A ‘Medium’ mesh and element type, CIRCU 94, and SOLID226 are selected in the CPC-FEM. A total of 2013 elements and 14,504 nodes are generated on the Hull PEH, while 6380 elements and 38,214 nodes are generated on the Cymbal PEH. The material properties of PZT are listed in Table 2. The bottom surface of the PEH’s frame is designated as the fixed support, establishing the boundary condition. An input force (i.e., 1 kN of impact force for 0.01 s) is applied at the top surface of the amplifier frame in the vertical axis. Since a safety factor of 2 is maintained throughout the FEA, a low stress level that is below half of the material’s fatigue limit can ensure the longevity and durability of the Hull PEH [33].
Figure 4 presents the stress distributions for both the Hull PEH and the benchmark Cymbal PEH under 1 kN of impact force. The stress distribution, especially the stress concentration region, is similar for both studies [29] if compared with the harmonic force of the same magnitude. The Hull PEH shows that the open-circuit peak voltage increases approximately linearly with increasing impact force from 10 N to 1 kN, as shown in Figure 5. The reason is that the stress and deformation levels in the PZT increase as the force rises. The Hull structure plays its role in amplifying the input force, causing the output force acting on the PZT to increase. According to the FEA, a high open-circuit peak voltage (i.e., 1031.12 V) is achieved under 1 kN of impact force. This shows that the Hull PEH has an excellent energy harvesting performance and force amplification effect under this range of forces.
Moreover, the modal analysis shows that the Hull PEH has a high natural frequency of over 300 Hz. Figure 6 shows its first mode occurs at 356.10 Hz, followed by frequencies of 633.09, 772.75, 797.36, 1293.80, and lastly 1569.60 Hz. In fact, the Hull PEH is designed for high-force, low-frequency environments, such as human foot strikes and vehicular excitation from roadway pavements, and other similar applications. In other words, the Hull PEH operates at a low and safe frequency range, which is less than 10 Hz [34].

3. Materials and Methods

3.1. Fabrication

The Hull and Cymbal amplifier frames were fabricated from stainless steel through wire cutting as shown in Figure 7. Two identical soft DL-53HD PZT plates (with size of 52 mm × 30 mm × 4 mm) were used in both PEHs to ensure a fair comparison. 3M Scotch-Weld™ DP-460 structural adhesive was applied to bond the frames and the PZT, since it offers higher shear and peel strengths, as well as better heat and chemical resistance. Laser welding was carried out to attach the substrates with the frame for the Cymbal PEH.

3.2. Experimental Setup

An impact loading test was conducted to verify the FEA voltage of the Hull PEH as shown in Figure 8. It was used to investigate the influence of the amount of applied load force on the voltage output of the Hull PEH, benchmark Cymbal PEH, and standalone PZT. A PCB® Piezotronics 086D20 impact hammer (PCB Piezotronics, Depew, NY, USA) with a sensitivity of 0.23 mV/N was used to induce the impact force on the PEHs. The PEH prototypes were fixed under a metal bar. The PZT wires were connected through National Instrument Data Acquisition (NI DAQ) devices (National Instruments, Austin, TX, USA), i.e., NI cDAQ-9174 and NI-9232 to a personal computer (PC), while the impact hammer was connected to a DAQ NI-9234.
DASYLab™ 10.0 software (National Instruments, Austin, TX, USA) was utilized to visualize and record the input force and the corresponding output voltage. The data sampling rate was configured at 2560 S/s, and the block size was set to 4096. Within DASYLab™, a statistical module showcased the maximum voltage value corresponding to the impact’s peak. To prevent overvoltage conditions beyond the DAQ devices’ input limits (i.e., ±30 V), a voltage divider was employed with ratios of measured resistance to total resistance such as 1:20, 1:33, 1:50, or 1:100 to scale down the measured voltage. A total resistance of 10 MΩ was used for the open-circuit test, while 50 kΩ was used in the power output tests via impedance matching. The impact force was manually adjusted from 10 N to 1 kN, and the result was recorded.

4. Experimental Results

4.1. Open-Circuit Voltage Test

The Hull PEH’s experimental open-circuit peak voltage result is shown with the best fit regression line in Figure 9. The influence of the amount of applied load force on the output voltage produced by the developed PEH is examined. It shows a positive correlation between the input impact force (ranging from 10 N to 1 kN) and the output voltage. This result agrees well with the mechanism of the Hull PEH since more deformation and stress accumulate at the PZT when a higher force is applied, leading to a higher output voltage. This correlation aligns well with the Hull PEH’s mechanism, where an increased loading force results in a greater deformation and stress accumulation at the PZT, thereby generating a higher output voltage.
The FEA and experimental open-circuit peak voltage results, under impact forces of 10 N, 50 N, 100 N, 200 N, 400 N, and 1 kN, are tabulated in Table 3. The experimental voltage for each force level is determined through interpolation, utilizing the equation of the best fit line, which is a necessary approach due to the difficulty in achieving precise impact force levels with hammer strikes. The experimental result agrees well with the FEA simulation. This proves that the developed CPC-FEM has high accuracy and reliability to demonstrate the real condition with less than 5.2% of deviation.
The energy harvesting performances of the Hull PEH, Cymbal PEH, and standalone PZT, measured in terms of output voltage, are compared in Figure 10. The Hull PEH shows a steeper gradient in the graph (i.e., 0.9775) than the Cymbal PEH, which has a gradient of 0.1436. Consequently, the Hull PEH exhibits a 6.8 times larger voltage output than the benchmark PEH. Furthermore, it demonstrates a great harvesting performance, which is 16.9 times higher than that of the standalone PZT by referring to the gradient of graph (i.e., 0.0578). This direct comparison of the open-circuit peak voltage reveals the remarkable energy harvesting capability of the Hull PEH. It shows a voltage amplification ratio of 16.9 when compared to the standalone PZT. This is despite the theoretical force amplification ratio for the Hull structure being reported as 9.72 in [29]. The deviation in results is caused by the different scales of amplification ratios in voltage, power output, and the force amplification effect faced by other researchers as well [31]. The Hull amplifier structure is proven to have a great effect in magnifying the input force and compressing the PZT on a larger scale.

4.2. Power Output Test

Impedance matching is carried out to determine the optimum resistance with the highest power output across a range of resistors (10 kΩ–1 MΩ). The maximum power output is gained at the optimum external resistance, which is matched with the internal impedance and the source impedance. It is found that the optimum load resistance for the Hull PEH remains the same throughout the range of impact forces, which is at 50 kΩ. It is not affected by the amount of force applied at the Hull PEH. In other words, the Hull PEH always produces the highest power output when it is connected across 50 kΩ of external load resistance under the impact force, as shown in Figure 11. Figure 12 shows the peak voltage and maximum power output across different resistances under 500 N and 1 kN impact forces, respectively. Both graphs clearly show that 50 kΩ is the optimum resistance with the highest maximum power outputs, which are 1.77 W under 500 N and 7.16 W under 1 kN of impact force.
These maximum power outputs are higher than those of the Cymbal structure, which are 0.04 W under 500 N and 0.19 W under 1 kN. The benchmark structure has the same optimum resistance at 50 kΩ as well under the impact force. The Hull PEH experimentally shows a better energy harvesting performance than the benchmark structure by producing a 37.68 times greater power output under 1 kN of impact force.

4.3. FE Model Validation with Experimental Result and Further Simulation Analysis

After verifying the optimum resistance experimentally, an FEA simulation across 50 kΩ is conducted to validate the power output and stress distribution. It shows a slight deviation of 3.5% in the peak voltage and 6.9% in the power output under 1 kN of impact force across the optimum resistance. Based on the maximum power of 7.69 W, the Hull PEH has a volume power density of 1232.37 kW/m3 under 1 kN of impact force, which is higher than the reported 1.817 kW/m3 in [29] under the harmonic force of same magnitude. This is due to the difference in optimum resistance (50 kΩ for impact force and 5.99 MΩ for harmonic force), and a higher voltage is obtained under the impact force.
The FEA is then conducted with a higher magnitude of force up to 2.5 kN to investigate the performance of the Hull PEH. The result is listed in Table 4. From the FEA result, the Hull PEH has a great advantage over the benchmark Cymbal PEH as its power output could continue increasing when the force increases up to 2.5 kN.
In contrast, the structural design of the Cymbal structure has to be adjusted so that it can safely work under higher forces. However, even if the thickness of the substrate and frame is increased to compensate for the increasing stress level, the Cymbal PEH still meets its power output limitation [35]. This is because the PZT material reaches the saturated state of its size under 2 kN of impact force. For instance, the voltage and power output of the Cymbal PEH stop increasing after 2 kN of impact force, as shown in Figure 13. It saturates at around 11.5 MPa of average PZT nodal stress in the FEA. Therefore, the PZT is said to be fully utilized by reaching the saturated tensile stress limit of its size.
Therefore, the Hull structure is concluded to have a greater capability to work in a higher-force environment since its PZT stress limit is 10 times higher than that in the tensile Cymbal structure of 17.5 MPa. There is room for improvement on the stress level in the Hull structure as the current design has an average PZT nodal stress of 33 Mpa under 1 kN of impact force.

4.4. Efficiency

The energy conversion efficiency, η, of the Hull PEH was calculated via equations from [22] based on the average input and output energies. The energy conversion efficiency was determined by analyzing the mechanical input response obtained from the accelerometer and impact hammer. Post-processing of the acceleration response retrieved from the accelerometer with a sensitivity of 100 mV/g was carried out. This involved double integration and the use of a band filter to derive the mechanical input displacement. Figure 14 and Figure 15 show the retrieved data and the calculation of the efficiency based on the input and output energy. The Hull PEH shows an efficiency of 84.38% under 1 kN of impact force, which is higher than that of a harmonic force with same magnitude (18.17%) [29].
This is because the impact force can produce a sudden and intense strain in PZT, potentially yielding a higher instantaneous voltage than the slower sinusoidal deformation from the harmonic force. Impact forces, being swift and short-lived, can produce higher strain rates in the PZT than a harmonic force, leading to increased voltage outputs. Furthermore, while an impact force concentrates its energy in a short period, a harmonic force spreads it out, possibly resulting in lower voltage spikes. Since the harmonic force does not align with the resonant frequency of the Hull PEH, its energy conversion is suboptimal, whereas an impact can stimulate multiple resonant modes. Moreover, sustained harmonic forces can induce energy losses through heating and increased damping, whereas the short duration of an impact might not give enough time for significant heating or energy loss due to damping. Hence, it is demonstrated that the Hull PEH exhibits better energy harvesting performance (i.e., higher voltage, power output, and efficiency) under the impact force compared to the harmonic force, which makes it suitable for foot-strike or vehicular excitation application. This promising green energy technology presents a sustainable path toward achieving Sustainable Development Goal 7 (SDG 7), offering a clean, innovative, and efficient method to ensure accessible and reliable energy for all.

5. Conclusions

In this study, an impact force is applied to study the performance of the compressive Hull PEH since it could represent the actual forcing environment better than the harmonic force. This is because the impact force has a much similar forcing profile to the targeted environment to demonstrate a foot strike or wheel rolling. The experimental result in terms of open-circuit output voltage proves the accuracy of the FEA with less than 5.2% of deviation under 10 N–1 kN of impact forces. It has a high natural frequency of over 300 Hz. In terms of harvesting performance, the Hull PEH exhibits a 6.8 times larger voltage output than the benchmark case and a 16.9 times greater voltage output than the standalone PZT. Thus, the Hull amplifier structure is proven to have a great effect in magnifying the input force and compressing the PZT on a larger scale. Under 1 kN of impact force, the Hull PEH generates around 1 kV of open-circuit peak voltage and 7.16 W of power output across 50 kΩ, which is 37.68 times higher than that of the benchmark Cymbal PEH.
From the validated FE model, the Hull PEH has a volume power density of 1232.37 kW/m3 based on the maximum power output and a higher loading capacity than the Cymbal PEH. It has a greater capability to work in a higher-force environment since the PZT’s compressive yield strength is 10 times higher than its tensile yield strength. It is also proven that the tensile-type benchmark structure will reach the saturated stress at a lower force with limited power output if compared with the Hull PEH. Moreover, an energy conversion efficiency of 84.38% is proven for the Hull PEH under 1 kN of impact force, which is higher than that of a harmonic force. This is due to the fact that impact forces induce sudden, high strain rates in PZT, potentially generating higher instantaneous voltages than the slower, spread-out deformations caused by harmonic forces, which might lead to a lower voltage and power output. In short, the harvesting performance of the Hull PEH is experimentally validated under the impact force, marking it a pivotal development in the journey toward a greener, sustainable future. It is concluded to have a better overall performance than the benchmark Cymbal PEH based on the voltage output, power output, loading capacity, and efficiency.

Author Contributions

Conceptualization, S.X.L. and S.Y.K.; formal analysis, S.X.L. and S.Y.K.; methodology, S.X.L. and S.Y.K.; software, S.X.L.; supervision, S.Y.K., Z.C.O. and M.F.S.; validation, S.X.L. and S.Y.K.; writing—original draft, S.X.L.; writing—review and editing, S.Y.K., Z.C.O., M.F.S. and Y.-H.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Universiti Malaya International Collaboration Grant (ST046-2022) under the SATU Joint Research Scheme Program; Universiti Malaya Research University Grant (RU Faculty) under grant number GPF081A-2018; and Ministry of Science and Technology (China) Grant MOST-107-2221-E-002-192-MY3.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgments

The authors wish to acknowledge the advice given by Advanced Shock and Vibration Research (ASVR) Group and Centre of Research Industry 4.0 (CRI 4.0) of Universiti Malaya. The suggestions and recommendations from reviewers are gratefully acknowledged.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Various types of mechanical amplifier structures in the piezoelectric energy harvester (reproduced from [22]).
Figure 1. Various types of mechanical amplifier structures in the piezoelectric energy harvester (reproduced from [22]).
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Figure 2. Artist’s impression of the Hull PEH as a sustainable power supply for the WSN of a traffic monitoring system.
Figure 2. Artist’s impression of the Hull PEH as a sustainable power supply for the WSN of a traffic monitoring system.
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Figure 3. Configuration of Hull PEH.
Figure 3. Configuration of Hull PEH.
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Figure 4. Stress distribution of (a) the overall Hull PEH and (b) its PZT as well as (c) the overall benchmark Cymbal PEH and (d) its PZT under 1 kN impact force.
Figure 4. Stress distribution of (a) the overall Hull PEH and (b) its PZT as well as (c) the overall benchmark Cymbal PEH and (d) its PZT under 1 kN impact force.
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Figure 5. FEA voltage output of the Hull PEH under various impact forces.
Figure 5. FEA voltage output of the Hull PEH under various impact forces.
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Figure 6. Natural frequencies of the Hull PEH from modal analysis.
Figure 6. Natural frequencies of the Hull PEH from modal analysis.
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Figure 7. Fabricated prototypes of (a) Hull PEH and (b) benchmark Cymbal PEH.
Figure 7. Fabricated prototypes of (a) Hull PEH and (b) benchmark Cymbal PEH.
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Figure 8. Experimental set up of impact test on Hull and Cymbal PEHs.
Figure 8. Experimental set up of impact test on Hull and Cymbal PEHs.
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Figure 9. Experimental open-circuit peak voltage of the Hull PEH under various impact forces.
Figure 9. Experimental open-circuit peak voltage of the Hull PEH under various impact forces.
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Figure 10. Experimental comparison of voltage output from the Hull PEH, the Cymbal PEH, and the standalone PZT plate under impact force.
Figure 10. Experimental comparison of voltage output from the Hull PEH, the Cymbal PEH, and the standalone PZT plate under impact force.
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Figure 11. Maximum power output of Hull PEH across several load resistances (10 kΩ to 200 kΩ) under various impact forces.
Figure 11. Maximum power output of Hull PEH across several load resistances (10 kΩ to 200 kΩ) under various impact forces.
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Figure 12. Impedance matching for Hull PEH under (a) 500 N and (b) 1 kN impact forces.
Figure 12. Impedance matching for Hull PEH under (a) 500 N and (b) 1 kN impact forces.
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Figure 13. Power output and the average PZT nodal stress of the Rectangular Cymbal PEH under different loading forces (reproduced from [35]).
Figure 13. Power output and the average PZT nodal stress of the Rectangular Cymbal PEH under different loading forces (reproduced from [35]).
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Figure 14. Raw data for Hull PEH’s energy conversion efficiency calculation, i.e., (a) force, (b) voltage, (c) acceleration, and (d) displacement under 1 kN impact force.
Figure 14. Raw data for Hull PEH’s energy conversion efficiency calculation, i.e., (a) force, (b) voltage, (c) acceleration, and (d) displacement under 1 kN impact force.
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Figure 15. (a) Force, (b) displacement, (c) input, and (d) output energy curves per cycle extracted from the raw data, and (e) the efficiency calculation for Hull PEH under 1 kN impact force.
Figure 15. (a) Force, (b) displacement, (c) input, and (d) output energy curves per cycle extracted from the raw data, and (e) the efficiency calculation for Hull PEH under 1 kN impact force.
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Table 1. Dimensions of Hull and Cymbal PEHs.
Table 1. Dimensions of Hull and Cymbal PEHs.
ParametersSymbolHull PEH [29]Cymbal PEH [32]
PZT length (mm)lPZT5252
PZT thickness (mm)tPZT44
Width (mm)w3030
Frame length (mm)l18652
Frame thickness (mm)t22
Cavity height (mm)h4.93.5
Horizontal linkage length (mm)lh46.518
Joint length (mm)lj76
Inclined angle (°)θ615
Apex length (mm)la-14
Substrate thickness (mm)ts-0.6
Table 2. Material properties of DL-53HD PZT.
Table 2. Material properties of DL-53HD PZT.
ParametersSymbols Values
Density (kg/m3)ρ7900
Elastic CoefficientStiffness constant
(×1010 N/m2)		C1116.9
C1211.8
C1310.9
C3312.3
C442.7
C552.7
C662.5
Elastic constant
(×10−12 m2/N)		S1115.1
S12−4.5
S13−9.4
S3324.8
S4437.1
S5537.1
S6639.2
Piezoelectric stress constant
(C/m2)		e31−12
e3318.2
e1521.9
Piezoelectric strain constant
(×10−12 C/N)		d31−300
d33680
d15810
Dielectric permittivityClamp dielectric constant, εS (At constant strain)ε111550
ε331390
Free dielectric constant, εT (At constant stress)ε113550
ε333850
Table 3. Experimental validation of open-circuit peak voltage of the Hull PEH under impact force.
Table 3. Experimental validation of open-circuit peak voltage of the Hull PEH under impact force.
Force (N)10501002004001000
FEA simulation Voc, peak (V)9.6448.8098.14197.81400.761031.12
Experimental Voc, peak (V)9.7848.8897.75195.50391.00977.50
Percentage error (%)1.400.150.391.172.445.20
Table 4. FEA result of the Hull PEH across 50 kΩ under higher impact forces.
Table 4. FEA result of the Hull PEH across 50 kΩ under higher impact forces.
Force (kN)1.02.02.5
Vpeak (V)619.961163.941624.14
Pmax (W)7.6927.1052.76
PZT maximum stress (MPa)62.37124.17163.63
Frame maximum stress (MPa)254.53610.85609.29
PZT average nodal stress (MPa)33.1056.2088.30
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MDPI and ACS Style

Long, S.X.; Khoo, S.Y.; Ong, Z.C.; Soong, M.F.; Huang, Y.-H. Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force. Sustainability 2023, 15, 15899. https://doi.org/10.3390/su152215899

AMA Style

Long SX, Khoo SY, Ong ZC, Soong MF, Huang Y-H. Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force. Sustainability. 2023; 15(22):15899. https://doi.org/10.3390/su152215899

Chicago/Turabian Style

Long, Su Xian, Shin Yee Khoo, Zhi Chao Ong, Ming Foong Soong, and Yu-Hsi Huang. 2023. "Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force" Sustainability 15, no. 22: 15899. https://doi.org/10.3390/su152215899

APA Style

Long, S. X., Khoo, S. Y., Ong, Z. C., Soong, M. F., & Huang, Y.-H. (2023). Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force. Sustainability, 15(22), 15899. https://doi.org/10.3390/su152215899

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