The effect of distance and dimensions of magnets on nonlinear behavior of piezomagnetoelastic bimorph energy harvester

Document Type : Research Article

Authors

1 Assistant Professor Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

2 Assistant Professor Faculty of Mechanical and Materials Engineering, Graduate University of Advanced Technology, Kerman, Iran

Abstract

This paper presents the effect of distance and dimensions of magnetson chaotic behavior and voltage level of a vibratory piezo-magneto-elastic bimorph energy harvesting system. The bimorph model comprises two iezoelectric
layers on a cantilever base structure with one tip magnet as well as two external magnets. The mathematical model is extracted by using distributed model.
The validity of the extracted model verified by previously published experimental results.In order to study the nonlinear dynamic of the bimorph, bifurcation diagram, phase plane portrait, time history response, Poincare map, power spectra diagram, and maximum Lyapunov exponents are used. In the bifurcation diagrams, the control parameters are the distances and dimensions of the magnets. It is shown that in the specific region of the control parameters, the sub-harmonic or super-harmonic behavior has minimum harvested voltage and irregular regions has maximum voltage. Also specific dimensions of tip magnet can influence greatly the dynamic behavior as well as output voltage. So these obtained results can give good insights about parameters identification and realization of the nonlinear behavior to reach the broadband higher harvested voltage of the system

Highlights

  • Nonlinear behavior of a piezomagnetoelastic bimorph energy harvester is studied.
  • Effects of magnet dimensions on the dynamics / harvested voltage are investigated.
  • Effect of magnets’ distances on the dynamics / harvested voltage is investigated.
  • Sub- or super- harmonic behavior is found to have the minimum harvested voltage.
  • Irregular behavior is found to have the maximum harvested voltage.

Keywords

Main Subjects


[1] M. Umeda, K. Nakamura, S. Ueha, Analysis of the transformation of mechanical impact energy to electric energy using piezoelectric vibrator, Japanese Journal of Applied Physics, 35 (1996) 3267.
[2] G.R. Samuel, Analysis of energy harvesting positive displacement motor, Journal of Energy Resources Technology, 129 (2007) 360-363.
[3] N.E. DuToit, B.L. Wardle, Experimental verification of models for microfabricated piezoelectric vibration energy harvesters, AIAA journal, 45 (2007) 1126-1137.
[4] X.d. Xie, Q. Wang, A mathematical model for piezoelectric ring energy harvesting technology from vehicle tires, International Journal of Engineering Science, 94 (2015) 113-127.
[5] N.V. Satpute, S.N. Satpute, L.M. Jugulkar, Hybrid electromagnetic shock absorber for energy harvesting in a vehicle suspension, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 10 (2016) 1-18.
[6] A. Abdelkefi, Aeroelastic energy harvesting: A review, International Journal of Engineering Science, 100 (2016) 112-135.
[7] M. Nouh, O. Aldraihem, A. Baz, Onset of Oscillations in Traveling Wave Thermo-Acoustic-Piezo-Electric Harvesters Using Circuit Analogy and SPICE Modeling, Journal of Dynamic Systems, Measurement, and Control, 136 (2014) 1-10.
[8] M. Mohammadpour, M. Dardel, M.H. Ghasemi, M.H. Pashaei, Nonlinear energy harvesting through a multimodal electro-mechanical system, Journal of Theoretical and Applied Vibration and Acoustics, 1 (2015) 73-84.
[9] S.-J. Jang, I.-H. Kim, K. Park, H.-J. Jung, An enhanced tunable rotational energy harvester with variable stiffness system for low-frequency vibration, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230 (2016) 732-736.
[10] P. Harte, E. Blokhina, O. Feely, D. Fournier-Prunaret, D. Galayko, Electrostatic vibration energy harvesters with linear and nonlinear resonators, International Journal of Bifurcation and Chaos, 24 (2014) 1430030.
[11] A. Erturk, D.J. Inman, Piezoelectric energy harvesting, John Wiley & Sons, 2011.
[12] S. Roundy, P.K. Wright, A piezoelectric vibration based generator for wireless electronics, Smart Materials and structures, 13 (2004) 1131-1144.
[13] N.E. Dutoit, B.L. Wardle, S.G. Kim, Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters, Integrated ferroelectrics, 71 (2005) 121-160.
[14] N.W. Hagood, W.H. Chung, A. Von Flotow, Modelling of piezoelectric actuator dynamics for active structural control, Journal of intelligent material systems and structures, 1 (1990) 327-354.
[15] H.A. Sodano, G. Park, D.J. Inman, Estimation of electric charge output for piezoelectric energy harvesting, Strain, 40 (2004) 49-58.
[16] A. Erturk, D.J. Inman, Issues in mathematical modeling of piezoelectric energy harvesters, Smart Materials and Structures, 17 (2008) 065016.
[17] A. Erturk, D.J. Inman, A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters, Journal of vibration and acoustics, 130 (2008) 041002.
[18] A. Erturk, D.J. Inman, An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations, Smart materials and structures, 18 (2009) 025009.
[19] C.D.M. Jr., A. turk, D.J. Inman, An electromechanical finite element model for piezoelectric energy harvester plates, Journal of Sound and Vibration, 327 (2009) 9-25.
[20] N.G. Elvin, A.A. Elvin, A coupled finite element—circuit simulation model for analyzing piezoelectric energy generators, Journal of Intelligent Material Systems and Structures, 20 (2009) 587-595.
[21] S. Zhao, A. Erturk, Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs, Smart Materials and Structures, 22 (2012) 015002.
[22] S.C. Stanton, A. Erturk, B.P. Mann, D.J. Inman, Nonlinear piezoelectricity in electroelastic energy harvesters: modeling and experimental identification, Journal of Applied Physics, 108 (2010) 074903.
[23] A. Abdelkefi, A.H. Nayfeh, M.R. Hajj, Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters, Nonlinear Dynamics, 67 (2012) 1147-1160.
[24] M. Ferrari, V. Ferrari, M. Guizzetti, D. Marioli, A single-magnet nonlinear piezoelectric converter for enhanced energy harvesting from random vibrations, Procedia Engineering, 5 (2010) 1156-1159.
[25] M. Ferrari, V. Ferrari, M. Guizzetti, B. Andò, S. Baglio, C. Trigona, Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters, Sensors and Actuators A: Physical, 162 (2010) 425-431.
[26] A. Triplett, D.D. Quinn, The effect of non-linear piezoelectric coupling on vibration-based energy harvesting, Journal of Intelligent Material Systems and Structures, 20 (2009) 1959-1967.
[27] R. Masana, M.F. Daqaq, Relative performance of a vibratory energy harvester in mono-and bi-stable potentials, Journal of Sound and Vibration, 330 (2011) 6036-6052.
[28] R. Masana, M.F. Daqaq, Energy harvesting in the super-harmonic frequency region of a twin-well oscillator, Journal of Applied Physics, 111 (2012) 044501.
[29] B.P. Mann, D.A. Barton, B.A. Owens, Uncertainty in performance for linear and nonlinear energy harvesting strategies, Journal of Intelligent Material Systems and Structures, 23 (2012) 1451-1460.
[30] M.F. Daqaq, R. Masana, A. Erturk, D.D. Quinn, On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion, Applied Mechanics Reviews, 66 (2014) 040801.
[31] A.J. Sneller, P. Cette, B.P. Mann, Experimental investigation of a post-buckled piezoelectric beam with an attached central mass used to harvest energy, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 225 (2011) 497-509.
[32] M. Coccolo, G. Litak, J.M. Seoane, M.A.F. Sanjuán, Energy harvesting enhancement by vibrational resonance, International Journal of Bifurcation and Chaos, 24 (2014) 1430019.
[33] M. Coccolo, G. Litak, J.M. Seoane, M.A.F. Sanjuán, Optimizing the electrical power in an energy harvesting system, International Journal of Bifurcation and Chaos, 25 (2015) 1550171.
[34] R.L. Harne, K.W. Wang, Axial suspension compliance and compression for enhancing performance of a nonlinear vibration energy harvesting beam system, Journal of Vibration and Acoustics, 138 (2016) 011004.
[35] J. Cao, S. Zhou, D.J. Inman, J. Lin, Nonlinear dynamic characteristics of variable inclination magnetically coupled piezoelectric energy harvesters, Journal of Vibration and Acoustics, 137 (2015) 021015.
[36] G. Caruso, Broadband energy harvesting from vibrations using magnetic transduction, Journal of Vibration and Acoustics, 137 (2015) 064503.
[37] P. Firoozy, S.E. Khadem, S.M. Pourkiaee, Broadband energy harvesting using nonlinear vibrations of a magnetopiezoelastic cantilever beam, International Journal of Engineering Science, 111 (2017) 113-133.
[38] T. Yildirim, M.H. Ghayesh, W. Li, G. Alici, A Nonlinearly Broadband Tuneable Energy Harvester, Journal of Dynamic Systems, Measurement, and Control, 139 (2017) 011008.
[39] T. Yildirim, M.H. Ghayesh, T. Searle, W. Li, G. Alici, A parametrically broadband nonlinear energy harvester, Journal of Energy Resources Technology, 139 (2017) 032001.
[40] D. Geiyer, J.L. Kauffman, Chaotification as a means of broadband energy harvesting with piezoelectric materials, Journal of Vibration and Acoustics, 137 (2015) 051005.
[41] J.J. Abbott, O. Ergeneman, M.P. Kummer, A.M. Hirt, B.J. Nelson, Modeling magnetic torque and force for controlled manipulation of soft-magnetic bodies, IEEE Transactions on Robotics, 23 (2007) 1247-1252.
[42] K. Yung, P. Landecker, D. Villani, An analytic solution for the force between two magnetic dipoles, Physical Separation in Science and Engineering, 9 (1998) 39-52.
[43] M. Beleggia, M. De Graef, Y.T. Millev, The equivalent ellipsoid of a magnetized body, Journal of Physics D: Applied Physics, 39 (2006) 891-899.
[44] D.J. Griffiths, Introduction to electrodynamics, in, 4th ed. Ltd., Publication, Prentice Hall 2013.
[45] P. Kim, J. Seok, A multi-stable energy harvester: Dynamic modeling and bifurcation analysis, Journal of Sound and Vibration, 333 (2014) 5525-5547.