This paper deals with analytical modelling of piezoelectric energy harvesting systems for generating useful electricity from ambient vibrations and comparing the usefulness of materials commonly used in designing such harvesters for energy harvesting applications. The kinetic energy harvesters have the potential to be used as an autonomous source of energy for wireless applications. Here in this paper, the considered energy harvesting device is designed as a piezoelectric cantilever beam with different piezoelectric materials in both bimorph and unimorph configurations. For both these configurations a single degree-of-freedom model of a kinematically excited cantilever with a full and partial electrode length respecting the dimensions of added tip mass is derived. The analytical model is based on Euler-Bernoulli beam theory and its output is successfully verified with available experimental results of piezoelectric energy harvesters in three different configurations. The electrical output of the derived model for the three different materials (PZT-5A, PZZN-PLZT and PVDF) and design configurations is in accordance with lab measurements which are presented in the paper. Therefore, this model can be used for predicting the amount of harvested power in a particular vibratory environment. Finally, the derived analytical model was used to compare the energy harvesting effectiveness of the three considered materials for both simple harmonic excitation and random vibrations of the corresponding harvesters. The comparison revealed that both PZT-5A and PZZN-PLZT are an excellent choice for energy harvesting purposes thanks to high electrical power output, whereas PVDF should be used only for sensing applications due to low harvested electrical power output.

Institute of Physics Czech Academy of Sciences 182 21 Prague Czech Republic

Laboratory of Energy Harvesting Institute of Solid Mechanics Mechatronics and Biomechanics Faculty of Mechanical Engineering Brno University of Technology 616 69 Brno Czech Republic

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Roundy S., Wright P.K., Rabaey J. A study of low level vibrations as a power source for wireless sensor nodes. Comput. Commun. 2003;26:1131–1144. doi: 10.1016/S0140-3664(02)00248-7. DOI

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. doi: 10.1109/JPROC.2008.927494. DOI

Roundy S., Wright P.K. A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct. 2004;13:1131–1142. doi: 10.1088/0964-1726/13/5/018. DOI

Hadas Z., Smilek J., Rubes O. Analyses of electromagnetic and piezoelectric systems for efficient vibration energy harvesting. In: Fonseca L., Prunnila M., Peiner E., editors. Smart Sensors, Actuators, and MEMS VIII. SPIE MICROTECHNOLOGIES; Barcelona, Spain: 2017.

Gljušćić P., Zelenika S., Blažević D., Kamenar E. Kinetic energy harvesting for wearable medical sensors. Sensors. 2019;19:4922. doi: 10.3390/s19224922. PubMed DOI PMC

Bai Y., Tofel P., Hadas Z., Smilek J., Lošák P., Skarvada P., Macku R. Investigation of a cantilever structured piezoelectric energy harvester used for wearable devices with random vibration input. Mech. Syst. Signal Process. 2018;106:303–318. doi: 10.1016/j.ymssp.2018.01.006. DOI

Paulo J., Gaspar P.D. Review and future trend of energy harvesting methods for portable medical devices. In: Ao S.I., Gelman L., Hukins D., editors. WCE 2010—World Congress on Engineering 2010. IAENG Society of Electrical Engineering; London, UK: 2010.

Zelenika S., Hadas Z., Bader S., Becker T., Gljušćić P., Hlinka J., Janak L., Kamenar E., Ksica F., Kyratsi T., et al. Energy Harvesting Technologies for Structural Health Monitoring of Airplane Components—A Review. Sensors. 2020;20:6685. doi: 10.3390/s20226685. PubMed DOI PMC

Duarte F., Ferreira A. Energy harvesting on railway tracks: State-of-the-art. Proc. Inst. Civ. Eng. Transp. 2017;170:123–130. doi: 10.1680/jtran.16.00016. DOI

Cahill P., Hanley C., Jaksic V., Mathewson A., Pakrashi V. Energy harvesting for monitoring bridges over their operational life; Proceedings of the 8th European Workshop on Structural Health Monitoring, EWSHM 2016; Bilbao, Spain. 5–8 July 2016; pp. 1–11.

Bowen C.R., Kim H.A., Weaver P.M., Dunn S. Piezoelectric and ferroelectric materials and structures for energy harvesting applications. Energy Environ. Sci. 2014;7:25–44. doi: 10.1039/C3EE42454E. DOI

Panda P.K., Sahoo B. PZT to lead free piezo ceramics: A review. Ferroelectrics. 2015;474:128–143. doi: 10.1080/00150193.2015.997146. DOI

Bai Y., Tofel P., Palosaari J., Jantunen H., Juuti J. A Game Changer: A Multifunctional Perovskite Exhibiting Giant Ferroelectricity and Narrow Bandgap with Potential Application in a Truly Monolithic Multienergy Harvester or Sensor. Adv. Mater. 2017;29:1700767. doi: 10.1002/adma.201700767. PubMed DOI

Tofel P., Machu Z., Chlup Z., Hadraba H., Drdlik D., Sevecek O., Majer Z., Holcman V., Hadas Z. Novel layered architecture based on Al2O3/ZrO2/BaTiO3 for SMART piezoceramic electromechanical converters. Eur. Phys. J. Spec. Top. 2019;228:1575–1588. doi: 10.1140/epjst/e2019-800153-0. DOI

Pozzi M., Canziani A., Durazo-Cardenas I., Zhu M. Experimental characterisation of macro fibre composites and monolithic piezoelectric transducers for strain energy harvesting. In: Kundu T., editor. Smart Structures (NDE) SPIE; Bellingham, DC, USA: 2012.

Sappati K.K., Bhadra S. Piezoelectric polymer and paper substrates: A review. Sensors. 2018;18:3605. doi: 10.3390/s18113605. PubMed DOI PMC

Song J., Zhao G., Li B., Wang J. Design optimization of PVDF-based piezoelectric energy harvesters. Heliyon. 2017;3:e00377. doi: 10.1016/j.heliyon.2017.e00377. PubMed DOI PMC

Kim M., Dugundji J., Wardle B.L. Efficiency of piezoelectric mechanical vibration energy harvesting. Smart Mater. Struct. 2015;24:055006. doi: 10.1088/0964-1726/24/5/055006. DOI

Erturk A., Inman D.J. Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. Smart Mater. Struct. 2008;17:065016. doi: 10.1088/0964-1726/17/6/065016. DOI

Liao Y., Liang J. Maximum power, optimal load, and impedance analysis of piezoelectric vibration energy harvesters. Smart Mater. Struct. 2018;27:075053. doi: 10.1088/1361-665X/aaca56. DOI

Li X., Upadrashta D., Yu K., Yang Y. Sandwich piezoelectric energy harvester: Analytical modeling and experimental validation. Energy Convers. Manag. 2018;176:69–85. doi: 10.1016/j.enconman.2018.09.014. DOI

Mendonca L.S., Martins L.T., Radecker M., Bisogno F., Killat D. Normalized Modeling of Piezoelectric Energy Harvester Based on Equivalence Transformation and Unit-Less Parameters. J. Microelectromech. Syst. 2019;28:666–677. doi: 10.1109/JMEMS.2019.2921649. DOI

Machů Z., Ševeček O., Hadas Z., Kotoul M. Modeling of electromechanical response and fracture resistance of multilayer piezoelectric energy harvester with residual stresses. J. Intell. Mater. Syst. Struct. 2020;31:2261–2287. doi: 10.1177/1045389X20942832. DOI

Meitzler A. 176-1987 IEEE Standard on Piezoelectricity. IEEE; New York, NY, USA: 1988.

Halliday D., Resnick R., Walker J. Fundamentals of Physics Extended. 9th ed. Wiley; Hoboken, NJ, USA: 2010.

Erturk A., Inman D.J. An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 2009;18:025009. doi: 10.1088/0964-1726/18/2/025009. DOI

Reddy J.N. Energy Principles and Variational Methods in Applied Mechanics. John Wiley & Sons, Ltd.; Hoboken, NJ, USA: 2017.

Flores-Domínguez M. Modeling of the Bending Stiffness of a Bimaterial Beam by the Approximation of One-Dimensional of Laminated Theory. J. Eng. Res. Appl. 2014;4:492–497.

Zhao J., You Z. Models for 31-Mode PVDF Energy Harvester for Wearable Applications. Sci. World J. 2014;2014:893496. doi: 10.1155/2014/893496. PubMed DOI PMC

Hadas Z., Rubes O., Tofel P., Machu Z., Riha D., Sevecek O., Kastyl J., Sobola D., Castkova K. Piezoelectric PVDF Elements and Systems for Mechanical Engineering Applications; Proceedings of the 2020 19th International Conference on Mechatronics—Mechatronika (ME); Prague, Czech Republic. 2–4 December 2020.

Rubes O., Machu Z., Sevecek O., Hadas Z. Crack Protective Layered Architecture of Lead-Free Piezoelectric Energy Harvester in Bistable Configuration. Sensors. 2020;20:5808. doi: 10.3390/s20205808. PubMed DOI PMC

Rubes O., Hadas Z. Design and Simulation of Bistable Piezoceramic Cantilever for Energy Harvesting from Slow Swinging Movement; Proceedings of the 2018 IEEE 18th International Conference on Power Electronics and Motion Control, PEMC 2018; Budapest, Hungary. 26–30 August 2018.

Rubes O., Brablc M., Hadas Z. Nonlinear vibration energy harvester: Design and oscillating stability analyses. Mech. Syst. Signal Process. 2019;125:170–184. doi: 10.1016/j.ymssp.2018.07.016. DOI

Fitzgerald P.C., Malekjafarian A., Bhowmik B., Prendergast L.J., Cahill P., Kim C.-W., Hazra B., Pakrashi V., Obrien E.J. Scour Damage Detection and Structural Health Monitoring of a Laboratory-Scaled Bridge Using a Vibration Energy Harvesting Device. Sensors. 2019;19:2572. doi: 10.3390/s19112572. PubMed DOI PMC

Sensors Special Issue: "Vibration Energy Harvesting for Wireless Sensors"