# Assessment of Impact Energy Harvesting in Composite Beams with Piezoelectric Transducers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Method

#### 2.1. Coupled Electromechanical System in Open-Circuit Conditions

_{i}and S

_{j}are the mechanical stress and engineering strain in vectorial notation; E

_{3}is the component of electric field vector along the thickness direction; D

_{3}is the electric displacement vector component; C

_{ij}is the elastic stiffness tensor; e

_{3j}is the piezoelectric tensor arising from the piezoelectric charge tensor and the stiffness tensor and ε

_{33}is the material electric permittivity. Superscripts E and S indicate constant electric field and strain conditions, respectively, and superscript T indicates matrix transposition. Equation (1) is formulated in a general manner to encompass the behavior of both a piezoelectric and a passive composite ply (e

_{mj}= 0). The electric field vector component E

_{3}is the gradient of the electric potential V along the thickness of the PE patch:

^{0}, v

^{0}, w

^{0}and β

_{x}, β

_{y}are displacements and rotations of the midsurface, respectively. As explicitly described in Section 2.2, a higher-order layerwise approximation of the through-thickness displacement field [47] is utilized at a specific stage of the method to directly provide the slope of transverse displacement along the longitudinal axis of the beam. The PE patch is modelled as a 3D solid continuum, perfectly bonded on the composite substrate, with electric potential as nodal DOF in addition to mechanical displacements.

_{0}, y

_{0}) are the coordinates of impact on the midsurface and k

_{y}is the contact stiffness derived by material and geometric properties [48]. The contact law of Equation (6) is represented schematically by interposition of a linear spring with stiffness k

_{y}between beam and impactor, as shown in Figure 3.

#### 2.2. Determination of the PEH Patch Model

_{p}are the length, width and thickness of the transducer, respectively.

_{s}and x

_{f}denoting the start and end of the patch in terms of length coordinate x.

- (a)
- Solving of Equation (5) for the free-vibration response of the open-circuit system in the frequency domain provides the eigenvectors, which are used for the formulation of the modal mass, damping, stiffness and force transformation matrices, respectively [52]:$$\begin{array}{c}\left[{\mathrm{M}}_{\mathrm{ffmod}}\right]={\left[\mathsf{\phi}\right]}^{\mathsf{{\rm T}}}\left[\mathrm{M}\right]\left[\mathsf{\phi}\right]\\ \left[{\mathrm{C}}_{\mathrm{ffmod}}\right]={\left[\mathsf{\phi}\right]}^{\mathsf{{\rm T}}}\left[\mathrm{C}\right]\left[\mathsf{\phi}\right]\\ \left[{\mathrm{K}}_{\mathrm{ffmod}}\right]={\left[\mathsf{\phi}\right]}^{\mathsf{{\rm T}}}\left[\mathrm{K}\right]\left[\mathsf{\phi}\right]\\ \left[{\mathrm{F}}_{\mathrm{sfmod}}\right]={\left[\mathsf{\phi}\right]}^{\mathsf{{\rm T}}}\left[\mathrm{F}\right]\end{array}$$
- (b)
- The modal matrices are used for determining η:$$\left[{\mathrm{M}}_{\mathrm{ffmod}}\right]\left\{\ddot{\mathsf{\eta}}\right\}+\left[{\mathrm{C}}_{\mathrm{ffmod}}\right]\left\{\dot{\mathsf{\eta}}\right\}+\left[{\mathrm{K}}_{\mathrm{ffmod}}\right]\left\{\mathsf{\eta}\right\}=\left\{{\mathrm{F}}_{\mathrm{sfmod}}\right\}u$$
- (c)
- The electromechanical coupling coefficient κ is provided by Equation (11) using PE properties, geometrical parameters and the slope of the modal transverse displacement. The latter is directly calculated in modal space, in addition to the eigenvectors and modal matrices, by implementing a C
^{1}-continuous 2D higher-order layerwise FE [47], which encompasses this slope as a nodal DOF. - (d)
- The electric current flowing through the PEH circuit is calculated using Equation (10). As an alternative to points (b–c), η may be derived at the point of excitation by means of a high-speed camera.
- (e)
- The PE transducer is modelled in the PEH circuit as a current source and a capacitor with C
_{p}appearing in Equation (8). - (f)
- The harvested power may be calculated as:$$\mathrm{P}\left(\mathrm{t}\right)=\frac{{{\displaystyle \int}}_{{\mathrm{t}}_{1}}^{{\mathrm{t}}_{2}}{\mathrm{V}}_{\mathrm{out}}\left(\mathrm{t}\right){\mathrm{I}}_{\mathrm{out}}\left(\mathrm{t}\right)\mathrm{dt}}{{\mathrm{t}}_{2}-{\mathrm{t}}_{1}}$$
_{out}and I_{out}are respectively the voltage and current in the discharging branch of the PEH circuit described in the following section.

#### 2.3. PEH Circuit

## 3. Experimental Configuration for Impact Testing

#### 3.1. Custom Impact Frame for Controlled Impact Velocity

^{5}samples/s per channel, and a digital I/O module (NI 9401) with a maximum sampling rate of 10

^{7}samples/s, while a rate of 10

^{4}samples/s is used for the control of the impactor. The software implemented for acquisition, control and storage of the signals is Labview FPGA [58]. The developed experimental configuration [59] enables impactor tip angle and velocity to be set by the test engineer to perform impact tests of various types [60] (see Appendix A). The displacement at the load application point is measured by processing images [61] acquired by a high-speed camera. A polyurethane tip was used in the impact tests. The positions of impactor and piezoelectric patch on the tested clamped composite beam are shown in Figure 2.

#### 3.2. Materials and Specimens

^{®}[62] (PI Ceramic GmbH, Lederhose, Germany) surface attached piezoelectric patch and lamination [−45/45/90

_{2}/0/90]

_{S}was studied. The patch consists of PIC255 piezoceramic embedded in polyimide. For the sake of simplicity, the piezoceramic part of the patch was modelled, and its properties are listed in Table 2. The elastic properties of the composite material considered were obtained from static tests [63] performed by the manufacturer (Hellenic Aerospace Industry S.A., Athens, Greeece). They were validated additionally by performing modal tests on the cantilever beam leading to measurement of the fundamental eigenfrequency at 89.7 Hz. A relatively large modal loss factor of η = 12.5% was assumed in the LP system, which includes the contribution of clamped support, viscoelastic material and intensive usage of the specimen in forced harmonic response tests [64]. The electromechanical properties of all materials considered are listed in Table 2.

## 4. Results and Discussion

_{y}was tuned by correlating model prediction with measured impact force and piezoelectric voltage time profiles, yielding a value of 500 N/m. In the prediction stage, the closed-circuit response was studied in three cases, each with a different electric component connected to the PE terminals: (i) a resistance of 10 kΩ; and (ii) the E-821.00 harvesting module twice, each time with a different charging subcircuit capacitor. The latter configuration was achieved by replacing the standard 200 μF capacitor with either of two other custom ones having a capacity of 100 μF and 1 nF, respectively.

#### 4.1. Open-Circuit Impact Response

#### 4.2. Closed-Circuit Resistive Impact Response

#### 4.3. Closed-Circuit PEH Response

## 5. Summary and Conclusions

- Predictions of the current methodology compared well with measurements of the electric response of the harvesting circuit, indicating its applicability in the design of PEH systems subjected to impact.
- Deviations between predictions and measurements were observed for the impact force due to the geometric clearance of the force sensor, approximation of impactor–beam contact stiffness and impactor deformability.
- Modification of the commercial PEH circuit in terms of capacity in the charging subcircuit led to harvesting of power in the impact conditions studied experimentally. The design of this modification was possible via the development of a circuit model equivalent to the commercial circuit in LTspice software, and respective verification.
- The harvested power increased with impactor mass and velocity beyond a threshold. Up to that threshold, no electric power produced due to the impact event and subsequent beam vibration could be extracted.
- A major capability of this methodology is the prediction of impact-force–time profile and stress distribution during impact events in composite beams with arbitrary lamination. In this context it can be used for the design of composite impact harvesters with piezoelectric patches, enabling the prediction of harvested power within applicable structural integrity limits.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Parameters of Impactor Mechanism

_{m}is the motor’s torque, ${\dot{\theta}}_{m}$ is the motor’s rotational speed, ${J}_{m}$ is the rotor’s inertia of the motor, ${b}_{m}$ is the viscous friction coefficient of the motor, $\dot{\theta}$ is the rotational speed of the impact pendulum (load), ${J}_{L}$ is the inertia of the load, ${b}_{L}$ is the viscous friction coefficient of the load, $n={R}_{2}/{R}_{1}$ is the planetary gearhead’s reduction, $i$ is the current that passes through the motor, ${K}_{T}$ is the torque constant, ${T}_{c}$ is the torque produced by the Coulomb friction, $u$ is the output torque after the gearhead, ${T}_{W}$ is the torque produced by the gravitational forces (weight) of the impact pendulum and ${b}_{e}$ is the equivalent coefficient of the viscous friction ${b}_{e}={n}^{2}\cdot {b}_{m}+{b}_{L}$.

T_{C} (Νm) | b (Nms) | M_{tot} (kg) | J_{m} (kgm^{2}) | J_{L} (kgm^{2}) | n | k_{T} (Nm/A) |
---|---|---|---|---|---|---|

0.068 | 0.46 | 0.367 | 3.47E-6 | 0.02 | 28 | 0.054 |

#### Appendix A.2. Control of Impactor Mechanism

**Figure A2.**Simplified closed-loop block diagram for a non-linear PV (or PD *) controller with weight compensation T

_{w}, where r(t) is the reference input signal, G

_{c}(s), G

_{p}(s) and H(s) are transfer functions of controller, plant and feedback loop, respectively, and T

_{d}is a term for the disturbances.

_{P}and K

_{V}are the gains of the controller, θ and θ

_{D}are actual and desired position of the impact pendulum, respectively, $\dot{\theta}$ is its rotational speed and T

_{W}is a term to compensate the torque produced by its weight.

#### Appendix A.3. Real-Time Implementation of the Control System

**Figure A4.**Flow chart of the integrated control and acquisition system, where DMA and FIFO denote direct memory access and first in, first out sequence, respectively.

Labview Real-Time Level | |

Control Loop | f_{control loop} = 1 kHz |

Labview FPGA Level | |

Encoder Measurements | f_{digital loop} = 10 kHz |

Analog Data Acquisition | f_{analog loop} = 16 kHz |

**Figure A5.**Implementation evidence of the developed real-time control system: (

**a**) position profile and (

**b**) velocity profile of the impactor.

**Figure A6.**Schematic representation of impactor tip angle, where v

_{lin}is linear velocity; v

^{x}

_{lin}is its x-component; p is the angle between x-axis and linear velocity vector; a is the distance between the tip of the impactor and point B, measured before testing and a1, a2 and a3 are rotation angles.

## References

- Kymissis, J.; Kendall, C.; Paradiso, J.; Gershenfeld, N. Parasitic power harvesting in shoes. In Proceedings of the Digest of Papers Second International Symposium on Wearable Computers (Cat. No.98EX215), Institute of Electrical and Electronics Engineers (IEEE), Pittsburgh, PA, USA, 6 August 2002. [Google Scholar]
- Elvin, N.G.; Elvin, A.; Spector, M. A self-powered mechanical strain energy sensor. Smart Mater. Struct.
**2001**, 10, 293–299. [Google Scholar] [CrossRef] - Cook-Chennault, K.; Thambi, N.; Sastry, A.M. Powering MEMS portable devices—A review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct.
**2008**, 17. [Google Scholar] [CrossRef] [Green Version] - Kim, H.S.; Kim, J.-H.; Kim, J. A review of piezoelectric energy harvesting based on vibration. Int. J. Precis. Eng. Manuf.
**2011**, 12, 1129–1141. [Google Scholar] [CrossRef] - Mitcheson, P.D.; Yeatman, E.; Rao, G.K.; Holmes, A.S.; Green, T. Energy harvesting from human and machine motion for wireless electronic devices. Proc. IEEE
**2008**, 96, 1457–1486. [Google Scholar] [CrossRef] [Green Version] - Safaei, M.; Sodano, H.A.; Anton, S.R. A review of energy harvesting using piezoelectric materials: State-of-the-art a decade later (2008–2018). Smart Mater. Struct.
**2019**, 28, 113001. [Google Scholar] [CrossRef] - Roundy, S.; Wright, P.K. A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct.
**2004**, 13, 1131–1142. [Google Scholar] [CrossRef] [Green Version] - Lu, F.; Lee, H.P.; Lim, S.P. Modeling and analysis of micro piezoelectric power generators for micro-electromechanical-systems applications. Smart Mater. Struct.
**2003**, 13, 57–63. [Google Scholar] [CrossRef] - Erturk, A.; Inman, D.J. Piezoelectric Energy Harvesting; John Wiley and Sons Ltd.: Oxford, UK, 2011. [Google Scholar]
- Erturk, A.; Hoffmann, J.; Inman, D.J. A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett.
**2009**, 94, 254102. [Google Scholar] [CrossRef] - Wickenheiser, A.M.; García, E. Broadband vibration-based energy harvesting improvement through frequency up-conversion by magnetic excitation. Smart Mater. Struct.
**2010**, 19, 065020. [Google Scholar] [CrossRef] - Masana, R.; Daqaq, M.F. Electromechanical modeling and nonlinear analysis of axially loaded energy harvesters. J. Vib. Acoust.
**2010**, 133, 011007. [Google Scholar] [CrossRef] - Harne, R.; Wang, K.W. A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct.
**2013**, 22. [Google Scholar] [CrossRef] - Jia, Y. Review of nonlinear vibration energy harvesting: Duffing, bistability, parametric, stochastic and others. J. Intell. Mater. Syst. Struct.
**2020**, 31, 921–944. [Google Scholar] [CrossRef] - Ottman, G.; Hofmann, H.; Bhatt, A.; Lesieutre, G. Adaptive piezoelectric energy harvesting circuit for wireless remote power supply. IEEE Trans. Power Electron.
**2002**, 17, 669–676. [Google Scholar] [CrossRef] [Green Version] - Ottman, G.K.; Hofmann, H.F.; Lesieutre, G. Optimized piezoelectric energy harvesting circuit using step-down converter in discontinuous conduction mode. IEEE Trans. Power Electron.
**2003**, 18, 696–703. [Google Scholar] [CrossRef] - Lefeuvre, E.; Badel, A.; Richard, C.; Petit, L.; Guyomar, D. A comparison between several vibration-powered piezoelectric generators for standalone systems. Sens. Actuators A Phys.
**2006**, 126, 405–416. [Google Scholar] [CrossRef] - Lefeuvre, E.; Audigier, D.; Richard, C.; Guyomar, D. Buck-boost converter for sensorless power optimization of piezoelectric energy harvester. IEEE Trans. Power Electron.
**2007**, 22, 2018–2025. [Google Scholar] [CrossRef] - Shen, H.; Qiu, J.; Ji, H.; Zhu, K.; Balsi, M. Enhanced synchronized switch harvesting: A new energy harvesting scheme for efficient energy extraction. Smart Mater. Struct.
**2010**, 19, 115017. [Google Scholar] [CrossRef] - Ramadass, Y.K.; Chandrakasan, A.P. An efficient piezoelectric energy harvesting interface circuit using a bias-flip rectifier and shared inductor. IEEE J. Solid State Circuits
**2010**, 45, 189–204. [Google Scholar] [CrossRef] [Green Version] - Tabesh, A.; Fréchette, L.G. A low-power stand-alone adaptive circuit for harvesting energy from a piezoelectric micropower generator. IEEE Trans. Ind. Electron.
**2010**, 57, 840–849. [Google Scholar] [CrossRef] [Green Version] - Liang, J.; Liao, W.-H. Impedance modeling and analysis for piezoelectric energy harvesting systems. IEEE ASME Trans. Mechatron.
**2011**, 17, 1145–1157. [Google Scholar] [CrossRef] - Huguet, T.; Lallart, M.; Badel, A. Bistable vibration energy harvester and SECE circuit: Exploring their mutual influence. Nonlinear Dyn.
**2019**, 97, 485–501. [Google Scholar] [CrossRef] - Guyomar, D.; Lallart, M. Recent progress in piezoelectric conversion and energy harvesting using nonlinear electronic interfaces and issues in small scale implementation. Micromachines
**2011**, 2, 274–294. [Google Scholar] [CrossRef] [Green Version] - Caliò, R.; Rongala, U.B.; Camboni, D.; Milazzo, M.; Stefanini, C.; De Petris, G.; Oddo, C.M. Piezoelectric energy harvesting solutions. Sensors
**2014**, 14, 4755–4790. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Linear Technology Corporation. Piezoelectric Energy Harvesting Power Supply; LTC-3588; Linear Technology Corporation: Norwood, MA, USA, 2010. [Google Scholar]
- PI Motion/Positioning. E-821 Electronic Module for Energy Harvesting Using Piezo Actuators for Energy Generation. 2014. Available online: https://www.physikinstrumente.com/en/products/controllers-and-drivers/piezo-drivers-for-open-loop-operation-of-piezo-actuators/e-821-electronic-module-for-energy-harvesting-608000/ (accessed on 28 September 2021).
- Plagianakos, T.S.; Papadopoulos, E.G. Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers. Int. J. Solids Struct.
**2014**, 51, 2713–2727. [Google Scholar] [CrossRef] [Green Version] - Umeda, M.; Nakamura, K.; Ueha, S. Analysis of the transformation of mechanical impact energy to electric energy using piezoelectric vibrator. Jpn. J. Appl. Phys.
**1996**, 35, 3267. [Google Scholar] [CrossRef] - Pozzi, M.; Zhu, M. Plucked piezoelectric bimorphs for knee-joint energy harvesting: Modelling and experimental validation. Smart Mater. Struct.
**2011**, 20, 055007. [Google Scholar] [CrossRef] [Green Version] - Renaud, M.; Fiorini, P.; van Schaijk, R.; van Hoof, C. Harvesting energy from the motion of human limbs: The design and analysis of an impact-based piezoelectric generator. Smart Mater. Struct.
**2009**, 18, 35001. [Google Scholar] [CrossRef] - Lee, E.H. The impact of a mass striking a beam. J. Appl. Mech.
**1940**, 7, A129–A138. [Google Scholar] [CrossRef] - Gu, L.; Livermore, C. Impact-driven, frequency up-converting coupled vibration energy harvesting device for low frequency operation. Smart Mater. Struct.
**2011**, 20, 045004. [Google Scholar] [CrossRef] - Basari, A.A.; Awaji, S.; Sakamoto, S.; Hashimoto, S.; Homma, B.; Suto, K.; Okada, H.; Okuno, H.; Kobayashi, K.; Kumagai, S. Evaluation on mechanical impact parameters in piezoelectric power generation. In Proceedings of the 10th Asian Control Conference (ASCC), Sabah, Malaysia, 31 May–3 June 2015; pp. 1–6. [Google Scholar]
- Doria, A.; Medè, C.; Desideri, D.; Maschio, A.; Codecasa, L.; Moro, F. On the performance of piezoelectric harvesters loaded by finite width impulses. Mech. Syst. Signal. Process.
**2018**, 100, 28–42. [Google Scholar] [CrossRef] - Jacquelin, E.; Adhikari, S.; Friswell, M. A piezoelectric device for impact energy harvesting. Smart Mater. Struct.
**2011**, 20, 105008. [Google Scholar] [CrossRef] - Martinez-Ayuso, G.; Friswell, M.I.; Adhikari, S.; Khodaparast, H.H.; Featherston, C.A. Energy harvesting using porous piezoelectric beam with impacts. Procedia Eng.
**2017**, 199, 3468–3473. [Google Scholar] [CrossRef] [Green Version] - Hunt, K.; Crossley, F.R.E. Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech.
**1975**, 42, 440–445. [Google Scholar] [CrossRef] - Fu, X.; Liao, W.-H. A dimensionless model of impact piezoelectric energy harvesting with dissipation. Act. Passiv. Smart Struct. Integr. Syst.
**2016**, 9799, 97991. [Google Scholar] [CrossRef] - Ferrari, M.; Cerini, F.; Ferrari, V. Autonomous sensor module powered by impact-enhanced energy harvester from broadband low-frequency vibrations. In Proceedings of the Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems, Barcelona, Spain, 16–20 June 2013; pp. 2249–2252. [Google Scholar] [CrossRef]
- Wong, C.H.; Dahari, Z. Development of vibration-based piezoelectric raindrop energy harvesting system. J. Electron. Mater.
**2017**, 46, 1869–1882. [Google Scholar] [CrossRef] - Feng, T.; Aono, K.; Covassin, T.; Chakrabartty, S. Self-powered monitoring of repeated head impacts using time-dilation energy measurement circuit. IEEE Trans. Biomed. Circuits Syst.
**2015**, 9, 217–226. [Google Scholar] [CrossRef] [PubMed] - Chen, N.; Jung, H.; Jabbar, H.; Sung, T.H.; Wei, T. A piezoelectric impact-induced vibration cantilever energy harvester from speed bump with a low-power power management circuit. Sens. Actuators A Phys.
**2017**, 254, 134–144. [Google Scholar] [CrossRef] - Dassault Systems. Abaqus/CAE User’s Guide, Version 6.14; Dassault Systems: Vienna, Austria, 2014. [Google Scholar]
- Available online: https://www.analog.com/en/analog-dialogue/articles/get-up-and-running-with-ltspice.html (accessed on 23 September 2021).
- Tiersten, H.F. Linear Piezoelectric Plate Vibrations; Springer Science: New York, NY, USA, 1969. [Google Scholar]
- Plagianakos, T.S.; Saravanos, D.A. High-order layerwise finite element for the damped free-vibration response of thick composite and sandwich composite plates. Int. J. Numer. Methods Eng.
**2009**, 77, 1593–1626. [Google Scholar] [CrossRef] - Yigit, A.; Christoforou, A. Impact dynamics of composite beams. Compos. Struct.
**1995**, 32, 187–195. [Google Scholar] [CrossRef] - Skrinjar, L.; Slavič, J.; Boltežar, M. A review of continuous contact-force models in multibody dynamics. Int. J. Mech. Sci.
**2018**, 145, 171–187. [Google Scholar] [CrossRef] - Yigit, A.S.; Christoforou, A.P.; Majeed, M.A. A nonlinear visco-elastoplastic impact model and the coefficient of restitution. Nonlinear Dyn.
**2011**, 66, 509–521. [Google Scholar] [CrossRef] - Siorikis, D.; Rekatsinas, C.; Christoforou, A.; Saravanos, D. Experimental and numerical investigation of contact laws for the rapid simulation of low-energy impacts on laminated composite plates. Compos. Struct.
**2017**, 168, 646–656. [Google Scholar] [CrossRef] - Walgrave, S.C.; Ehlbeck, J.M. Understanding modal analysis. SAE Tech. Pap. Ser.
**1978**, 87. [Google Scholar] [CrossRef] - Plagianakos, T.; Lika, K.; Papadopoulos, E.G. Low-velocity impact response of smart sandwich composite plates with piezoelectric transducers: Modeling and experiments. J. Intell. Mater. Syst. Struct.
**2016**, 27, 774–785. [Google Scholar] [CrossRef] - Maxon Motor. ESCON Module 50/5 Servo Controller-Hardware Reference; Maxon Motor: Sachseln, Switzerland, 2014. [Google Scholar]
- Available online: https://www.botasys.com/ (accessed on 9 October 2020).
- Nise, N.S. Control System Engineering, 9th ed.; John Wiley & Sons: Oxford, UK, 2019. [Google Scholar]
- Available online: https://www.ni.com/en-us/support/model.crio-9074.html (accessed on 18 September 2021).
- National Instruments Co. LabVIEW FPGA Course Manual; National Instruments Co.: Austin, TX, USA, 2009. [Google Scholar]
- Karydis-Karandreas, P. Modeling and Control of an Impact Pendulum for Impact Testing of Plates with Pi-Ezoelectric Transducers. Master’s Thesis, National Technical University of Athens, Athens, Greece, 2019. [Google Scholar]
- Christoforou, A.P.; Yigit, A. Characterization of impact in composite plates. Compos. Struct.
**1998**, 43, 15–24. [Google Scholar] [CrossRef] - Komitopoulos, S. Active Vibration Control of Composite Beams Using Piezoelectric Transducers and Real-Time Software. Master’s Thesis, National Technical University of Athens, Athens, Greece, 2021. [Google Scholar]
- Available online: https://www.piceramic.com/en/ (accessed on 27 September 2020).
- Karachalios, E.; Muñoz, K.; Jimenez, M.; Prentzias, V.; Goossens, S.; Geernaert, T.; Plagianakos, T.S. LRI-fabricated composite demonstrators for an aircraft fuselage on the basis of a Building Block design approach. Compos. Part. C Open Access
**2021**, 6, 100178. [Google Scholar] [CrossRef] - Plagianakos, T.S.; Margelis, N.; Leventakis, N.; Bolanakis, G.; Vartholomeos, P.; Papadopoulos, E.G. Finite element-based assessment of energy harvesting in composite beams with piezoelectric transducers. Proc. Inst. Mech. Eng. Part. L J. Mater. Des. Appl.
**2021**. [Google Scholar] [CrossRef]

**Figure 6.**Experimental configuration for impact tests: (

**a**) schematic representation with measurement system, (

**b**) photo of impact frame with beam specimen, (

**c**) PEH circuit including an E-821.00 module.

**Figure 7.**Time history of predicted and measured impact response (v

^{i}= 0.75 m/s) in open-circuit configuration: (

**a**) impact force, (

**b**) tip displacement and (

**c**) electric potential at piezoelectric terminals.

**Figure 8.**Impact response in a resistive circuit with R = 10 kΩ: (

**a**) resistor voltage, (

**b**) circuit current.

**Figure 9.**Predicted and measured signals at the piezoelectric terminals of the PEH circuit with a 100 μF capacitor in the case of impact: (

**a**) voltage, (

**b**) current.

**Figure 10.**Predicted and measured signals at the capacitor of the PEH circuit with a 100 μF capacitor in the case of impact: (

**a**) voltage, (

**b**) current.

**Figure 11.**Predicted and measured voltage in the output of the discharging subcircuit in the case of a PEH circuit with capacity of 2.7 μF.

**Figure 14.**Longitudinal stress distribution in ply 3 of a composite beam at maximum impact force during the impact of a 0.3 kg mass hitting with 4 m/s initial velocity.

Parameter | Value (mm) | Parameter | Value (mm) |
---|---|---|---|

Beam length L | 128 | PE patch length L_{p} | 50 |

Beam width b | 37 | PE patch width b_{p} | 30 |

Beam thickness h | 2.15 | PE patch thickness h_{p} | 0.2 |

Distance from support d_{1} | 5.5 | Distance from free end d_{2} | 10 |

Property | Composite Material | Piezoelectric Material |
---|---|---|

Density (kg/m^{3}) | 1554 | 7800 |

Elastic Properties | ||

E_{11} (GPa) | 138.40 | 62.10 |

E_{22} (GPa) | 8.50 | 62.10 |

E_{33} (GPa) | 8.50 | 48.30 |

G_{12} (GPa) | 4.30 | 23.20 |

G_{13} (GPa) | 4.30 | 21.30 |

G_{23} (GPa) | 4.30 | 21.30 |

ν_{12} | 0.31 | 0.33 |

ν_{13} | 0.31 | 0.43 |

ν_{23} | 0.31 | 0.43 |

Piezoelectric Properties | ||

d_{31} (10^{−12} m/V) | - | −191 |

d_{32} (10^{−12} m/V) | - | −191 |

d_{33} (10^{−12} m/V) | - | 409 |

Dielectric Properties (ε^{0} = 8.85 × 10^{−12} F/m) | ||

ε_{33}/ε^{0} | 3.5 | 1832 * |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Margelis, N.; Plagianakos, T.S.; Karydis-Karandreas, P.; Papadopoulos, E.G.
Assessment of Impact Energy Harvesting in Composite Beams with Piezoelectric Transducers. *Sensors* **2021**, *21*, 7445.
https://doi.org/10.3390/s21227445

**AMA Style**

Margelis N, Plagianakos TS, Karydis-Karandreas P, Papadopoulos EG.
Assessment of Impact Energy Harvesting in Composite Beams with Piezoelectric Transducers. *Sensors*. 2021; 21(22):7445.
https://doi.org/10.3390/s21227445

**Chicago/Turabian Style**

Margelis, Nikolaos, Theofanis S. Plagianakos, Panagiotis Karydis-Karandreas, and Evangelos G. Papadopoulos.
2021. "Assessment of Impact Energy Harvesting in Composite Beams with Piezoelectric Transducers" *Sensors* 21, no. 22: 7445.
https://doi.org/10.3390/s21227445