Abstract
This chapter explores the nonlinear dynamics of a bistable piezo-magneto-elastic energy harvester with the objective of determining the influence of external force parameters on the system response. Time series, phase space trajectories, Poincaré maps and bifurcation diagrams are employed in order to reveal system dynamics complexity and nonlinear effects, such as chaos incidence and hysteresis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M.A.A. Abdelkareem, L. Xu, M.K.A. Ali, A. Elagouz, J. Mi, S. Guo, Y. Liu, L. Zuo, Vibration energy harvesting in automotive suspension system: a detailed review. Appl. Energy 229, 672–699 (2018)
C.H.C.C. Basqueroto, F.R. Chavarette, S. da Silva, Analysis of bistable and chaotic piezoelectric energy harvesting device coupled with diode bridge rectifier. Int. J. Pure Appl. Math. 98, 275–289 (2015)
M. Belhaq, M. Hamdi, Energy harvesting from quasi-periodic vibrations. Nonlinear Dyn. 86, 2193–2205 (2016)
M. Borowiec, Energy harvesting of cantilever beam system with linear and nonlinear piezoelectric model. Eur. Phys. J. Spec. Top. 224(14), 2771–2785 (2015)
S. Bradai, S. Naifar, C. Viehweger, O. Kanoun, G. Litak, Nonlinear analysis of an electrodynamic broadband energy harvester. Eur. Phys. J. Spec. Top. 224(14), 2919–2927 (2015)
M.A. Clementino, R. Reginatto, S. da Silva, Modeling of piezoeletric energy harvesting considering the dependence of the rectifier circuit. J. Intell. Mater. Syst. Struct. 36, 283–292 (2014)
F. Cottone, H. Vocca, L. Gammaitoni, Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601 (2009)
H.L. Dai, Y.W. Yang, A. Abdelkefi, L. Wang, Nonlinear analysis and characteristics of inductive galloping energy harvesters. Commun. Nonlinear Sci. Numer. Simul. 59, 580–591 (2018)
A. Erturk, J. Hoffmann, D.J. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94, 254102 (2009)
F.M. Foong, C.K. Thein, D. Yurchenko, On mechanical damping of cantilever beam-based electromagnetic resonators. Mech. Syst. Signal Process. 119, 120–137 (2019)
M.I. Friswell, S.F. Ali, O. Bilgen, S. Adhikari, A.W. Lees, G. Litak, Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass. J. Intell. Mater. Syst. Struct. 23(13), 1505–1521 (2012)
Z. Ghouli, M. Hamdi, F. Lakrad, M. Belhaq, Quasiperiodic energy harvesting in a forced and delayed Duffing harvester device. J. Sound Vib. 407, 271–285 (2017)
J.A.B. Gripp, L.C.S. Góes, O. Heuss, F. Scinocca, An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure. Smart Mater. Struct. 24(12), 125017 (2015)
Z. Hadas, L. Janak, J. Smilek, Virtual prototypes of energy harvesting systems for industrial applications. Mech. Syst. Signal Process. 110, 152–164 (2018)
E. Halvorsen, G. Litak, Statistics of a noise-driven elastic inverted pendulum. Eur. Phys. J. Appl. Phys. 70(1), 10901 (2015)
P. Harris, G. Litak, J. Iwaniec, C.R. Bowen, Recurrence plot and recurrence quantification of the dynamic properties of cross-shaped laminated energy harvester. Appl. Mech. Mater. 849, 95–105 (2016)
P. Holmes, A nonlinear oscillator with a strange attractor. Philos. Trans. R. Soc. A 292, 429–448 (1979)
S. Ju, C. Ji, Impact-based piezoelectric vibration energy harvester. Appl. Energy 214, 139–151 (2018)
P. Kamalinejad, C. Mahapatra, Z. Sheng, S. Mirabbasi, V.C.M. Leung, Y.L. Guan, Wireless energy harvesting for the internet of things. IEEE Commun. Mag. 53, 102–108 (2015)
S. Kato, S. Ushiki, A. Masuda, A broadband energy harvester using leaf springs and stoppers with response stabilization control. J. Phys. Conf. Ser. 1052, 012083 (2018)
J.M. Kluger, T.P. Sapsis, A.H. Slocum, Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams. J. Sound Vib. 341, 174–194 (2015)
I. Kovacic, M. Brennan, The Duffing Equation: Nonlinear Oscillators and their Behavior (Wiley, 2011)
A. Kumar, R. Kiran, V.S. Chauhan, R. Kumar, R. Vaish, Piezoelectric energy harvester for pacemaker application: a comparative study. Mater. Res. Express 5, 075701 (2018)
Y. Liao, J. Liang, Unified modeling, analysis and comparison of piezoelectric vibration energy harvesters. Mech. Syst. Signal Process. 123, 403–425 (2019)
G. Litak, M.I. Friswell, S. Adhikari, Regular and chaotic vibration in a piezoelectric energy harvester. Meccanica 51(5), 1017–1025 (2016)
G. Litak, A. Rysak, M. Borowiec, M. Scheffler, J. Gier, Vertical beam modal response in a broadband energy harvester. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn. 230 (2016)
V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr., Numerical study of parameters influence over the dynamics of a piezo-magneto-elastic energy harvesting device (In XXXVII Congresso Nacional de Matemática Aplicada e Computacional, São José dos Campos, Brazil, 2017)
V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr, On the nonlinear dynamics of a bi-stable piezoelectric energy harvesting device, in 24th ABCM International Congress of Mechanical Engineering (COBEM 2017) (Curitiba, Brazil, 2017)
V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr, Analysis of the nonlinear dynamics of a bistable energy harvesting system with colored noise disturbances, in Conference of Computational Interdisciplinary Science (CCIS 2019) (2019)
Q. Lu, L. Liu, F. Scarpa, J. Leng, Y. Liu, A novel composite multi-layer piezoelectric energy harvester. Compos. Struct. 201, 121–130 (2018)
W. Martens, U. von Wagner, G. Litak, Stationary response of nonlinear magneto-piezoelectric energy harvester systems under stochastic excitation. Eur. Phys. J. Spec. Top. 222(7), 1665–1673 (2013)
F.C. Moon, P.J. Holmes, A magnetoelastic strange attractor. J. Sound Vib. 65, 275–296 (1979)
R. Naseer, H.L. Dai, A. Abdelkefi, L. Wang, Piezomagnetoelastic energy harvesting from vortex-induced vibrations using monostable characteristics. Appl. Energy 203, 142–153 (2017)
D. Pan, F. Dai, Design and analysis of a broadband vibratory energy harvester using bi-stable piezoelectric composite laminate. Energy Convers. Manag. 169, 149–160 (2018)
T. Pereira, A. Paula, A. Fabro, M. Savi. Random effects in a nonlinear vibration-based piezoelectric energy harvesting system. Int. J. Bifurc. Chaos, (in press) (2019)
J.V.L.L. Peterson, V.G. Lopes, A. Cunha Jr., Dynamic analysis and characterization of a nonlinear bi-stable piezo-magneto-elastic energy harvester, in MATEC Web of Conferences vol. 241 (2018), p. 01001
D. Puspitarini, A. Suzianti, H. Al Rasyid, Designing a sustainable energy-harvesting stairway: determining product specifications using triz method. Procedia Soc. Behav. Sci. 216, 938–947, in Urban Planning and Architectural Design for Sustainable Development (UPADSD) (2016)
T.M.P. Silva, M.A. Clementino, A. Erturk, C. de Marqui Jr., Equivalent electrical circuit framework for nonlinear and high quality factor piezoelectric structures. Mechatronics 54, 133–143 (2018)
S. Stoykov, G. Litak, E. Manoach, Vibration energy harvesting by a timoshenko beam model and piezoelectric transducer. Eur. Phys. J. Spec. Top. 224(14), 2755–2770 (2015)
M.A. Trindade, C.C. Pagani, L.P.R. Oliveira, Semi-modal active vibration control of plates using discrete piezoelectric modal filters. J. Sound Vib. 351, 17–28 (2015)
K. Vijayan, M.I. Friswell, H. Haddad Khodaparast, S. Adhikari, Non-linear energy harvesting from coupled impacting beams. Int. J. Mech. Sci. 96-97, 101–109 (2015)
C. Wang, Q. Zhang, W. Wang, J. Feng, A low-frequency, wideband quad-stable energy harvester using combined nonlinearity and frequency up-conversion by cantilever-surface contact. Mech. Syst. Signal Process. 112, 305–318 (2018)
C. Wei, X. Jing, A comprehensive review on vibration energy harvesting: modelling and realization. Renew. Sustain. Energy Rev. 74, 1–18 (2017)
X.D. Xie, Q. Wang, S.J. Wang, Energy harvesting from high-rise buildings by a piezoelectric harvester device. Energy 93, 1345–1352 (2015)
Z. Zhou, W. Qin, W. Du, P. Zhu, Q. Liu, Improving energy harvesting from random excitation by nonlinear flexible bi-stable energy harvester with a variable potential energy function. Mech. Syst. Signal Process. 115, 162–172 (2019)
Acknowledgements
The authors acknowledge the support given to this research by the funding agencies Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ) under grants E-26/010.002.178/2015 and E-26/010.000.805/2018, and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES)–Finance Code 001.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Lopes, V.G., Peterson, J.V.L.L., Cunha Jr., A. (2019). Nonlinear Characterization of a Bistable Energy Harvester Dynamical System. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_3
Download citation
DOI: https://doi.org/10.1007/978-981-13-9463-8_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9462-1
Online ISBN: 978-981-13-9463-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)