Abstract
For the designed nonlinear hybrid piezoelectric (PE)–electromagnetic (EM) energy harvester, electromechanical coupling state equations are established at stochastic excitation, and vibration response, output mean power, voltage and current are derived by statistical linearization method. Then, effects of nonlinear strength, load resistance and excitation spectral density on vibration response and electric output of nonlinear hybrid energy harvester are studied by theoretical analysis, simulation and experimental test. It is obtained that mean power of nonlinear hybrid energy harvester increases linearly with acceleration spectral density; the bigger nonlinear strength, the bigger output power of energy harvester and the lower resonant frequency are; besides, mean amplitude of nonlinear hybrid energy harvester reaches the minimum at PE optimal load, but it increases with EM load increasing. Compared with linear hybrid energy harvester, the resonant frequency of nonlinear energy harvester can be decreased by 57%, while output power can be increased by 72%.
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References
Al-Ashtari W, Hunstig M, Hemsel T (2012) Frequency tuning of piezoelectric energy harvesters by magnetic force. Smart Mater Struct 21:035019
Blystad LCJ, Halvorsen E, Husa S (2010) Piezoelectric MEMS energy harvesting systems driven by harmonic and random vibrations. IEEE Trans Ultrason Ferroelectr Freq Control 57(4):908–919
Cammarano A, Neild SA, Burrow SG (2014) Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity. J Intell Mater Syst Struct 25(14):1757–1770
Challa VR, Prasad MG, Shi Y (2008) A vibration energy harvesting device with bidirectional resonance frequency tunability. Smart Mater Struct 17:015035
Cottone F, Gammaitoni L, Vocca H et al (2012) Piezoelectric buckled beams for random vibration energy harvesting. Smart Mater Struct 21:035021
Daqaq MF (2011) Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise. J Sound Vib 330(11):2554–2564
Daqaq MF (2012) On intentional introduction of stiffness nonlinearities for energy harvesting under white Gaussian excitations. Nonlinear Dyn 69:1063–1079
Erturk A, Inman DJ (2011) Piezoelecric energy harvesting. Wiley, Chichester
Ferrari M, Ferrari V, Guizzetti M (2010) Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters. Sens Actuat A 162:425–431
Foisal ARM, Hong C, Chung GS (2012) Multi-frequency electromagnetic energy harvester using a magnetic spring cantilever. Sens Actuat A 182:106–113
Gradshtenyn IS, Ryzhik IM (1994) Table of integrals series, and products. Academic, New York, pp 130–132
Green PL, Worden K, Atallah K (2012) The benefits of Duffing-type nonlinearities and electrical optimisation of a mono-stable energy harvester under white Gaussian excitations. J Sound Vib 331(20):4504–4517
Green PL, Papatheou E, Sims ND (2013) Energy harvesting from human motion and bridge vibrations: an evaluation of current nonlinear energy harvesting solutions. J Intell Mater Syst Struct 24(12):1494–1505
Halvorsen E (2008) Energy harvesters driven by broadband random vibrations. J Microelectromech Syst 17(5):1061–1071
Jackson WC, Brian KH, Emiliano SR (2013) Experimental analysis of a piezoelectric energy harvesting system for harmonic, random, and sine on random vibration. Adv Acoust Vib. doi:10.1155/2013/241025
Jiang WA, Chen LQ (2013) Energy harvesting of monostable Duffing oscillator under Gaussian white noise excitation. Mech Res Commun 53:85–91
Jiang WA, Chen LQ (2014) An equivalent linearization technique for nonlinear piezoelectric energy harvesters under Gaussian white noise. Commun Nonlinear Sci Numer Simul 19:2897–2904
Karami MA, Inman DJ (2011) Electromechanical modeling of the low-frequency zigzag micro-energy harvester. J Intell Mater Syst Struct 22:271–282
Kumar P, Narayanan S, Adhikari S et al (2014) Fokker–Planck Eq. analysis of randomly excited nonlinear energy harvester. J Sound Vib 333(7):2040–2053
Li P, Gao S, Niu S et al (2014) An analysis of the coupling effect for a hybrid piezoelectric and electromagnetic energy harvester. Smart Mater Struct 23(6):065016
Li P, Gao S, Cai H (2015) Modeling and analysis of hybrid piezoelectric and electromagnetic energy harvesting from random vibrations[J]. Microsyst Technol 21(2):401–414
Li P, Gao S, Cai H (2016) Theoretical analysis and experimental study for nonlinear hybrid piezoelectric and electromagnetic energy harvester. Microsyst Technol 22:727–739
Liu CH (2008) Stochastic process, 4th edn. Huazhong University of Science and Technology Press, Wuhan
Liu H, Lee C, Kobayashi T (2012) A new S-shaped MEMS PZT cantilever for energy harvesting from low frequency vibrations below 30 Hz. Microsyst Technol 18:497–506
Mann BP, Owens BA (2010) Investigations of a nonlinear energy harvester with a bistable potential well. J Sound Vib 329:1215–1226
Maryam GT, Stephen JE (2014) Extending the dynamic range of an energy harvester using nonlinear damping. J Sound Vib 3:623–629
Marzencki M, Defosseux M, Basrour S (2009) MEMS vibration energy harvesting devices with passive resonance frequency adaptation capability. J Microelectromech Syst 18:1444–1453
Meimukhin D, Cohen N, Bucher I (2013) On the advantage of a bistable energy harvesting oscillator under band-limited stochastic excitation. J Intell Mater Syst Struct 24(14):1736–1746
Owens BAM, Mann BP (2012) Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting. J Sound Vib 331:922–937
Pellegrini SP, Tolou N, Schenk M (2013) Bistable vibration energy harvesters: a review. J Intell Mater Syst Struct 24:1303–1312
Sebald G, Kuwano H, Guyomar D (2011) Experimental Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mater Struct 20:102001
Serre C, Rodríguez AP, Fondevilla N (2007) Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators. Microsyst Technol 13:1655–1661
Shan X, Guan S, Liu Z (2013) A new energy harvester using a piezoelectric and suspension electromagnetic mechanism. Journal of Zhejiang University Science A 14:890–897
Spreemann D, Manoli Y (2012) Electromagnetic vibration energy harvesting devices. Springer, Germany
Tiwari R, Buch N, Garcia E (2014) Energy balance for peak detection method in piezoelectric energy harvester. J Intell Mater Syst Struct 25:1024–1035
Tongji University, Department of Mathematics (2007) Higher mathematics. High Education Press, China
Torsten R, Armaghan S (2010) Analysis and modelling towards hybrid piezo-electromagnetic vibrating energy harvesting devices. AIP Conf Proc 81:81–85
Wu X, Khaligh A, Xu Y (2008) Modeling, design and optimization of hybrid electromagnetic and piezoelectric MEMS energy scavengers. In: IEEE 2008 custom intergrated circuits conference, pp 177–181
Yang X, Wang Y, Cao Y (2014) A new hybrid piezoelectric–electromagnetic vibration-powered generator and its model and experiment research. IEEE Trans Appl Superconduct 24:1–4
Zhuang BZ, Chen NL (1986) Theory and application of nonlinear random vibration. Zhe Jiang University Press, China
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Li, P., Gao, S., Zhou, X. et al. Analytical modeling, simulation and experimental study for nonlinear hybrid piezoelectric–electromagnetic energy harvesting from stochastic excitation. Microsyst Technol 23, 5281–5292 (2017). https://doi.org/10.1007/s00542-017-3329-5
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DOI: https://doi.org/10.1007/s00542-017-3329-5