Analytical Solution and Optimization for Energy Harvesting from Nonlinear Vibration of Magneto- Electro- Elastic Plate

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran

2 Department of Electrical Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran

Abstract

 In the present paper, a mathematical model has been provided for a magneto-electro-elastic plate to investigate its energy harvesting in nonlinear transverse vibration. The nonlinear equations of motion of a magneto-electro-elastic plate have been used based on the Kirchhoff plate theory. These equations have been reduced to an ordinary deferential equations using Airy stress function and Galerkin Method. The equivalent electrical circuit of the structure is developed. A closed form solution has been obtained for the output power of the harvester using the method of multiple scales. The obtained results are compared with those of finite element method and a good agreement observed between the results of displacement and voltage. By introducing an analytical relation for the power as cost function, the Genetic Algorithm method is applied to optimize the best parameters of the harvester which gives the maximum power. The effect of various parameters of the harvester, such as dimension and thickness, on the power is investigated and the results are discussed.

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References

[1] C. Zhang, J. Yang, W. Chen, Harvesting magnetic energy using extensional vibration of laminated magnetoelectric plates, Applied Physics Letters, 95(1) (2009) 013511.
[2] C.J. Rupp, A. Evgrafov, K. Maute, M.L. Dunn, Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells, Journal of Intelligent Material Systems and Structures, 20(16) (2009) 1923-1939.
[3] C.D.M. Junior, A. Erturk, D.J. Inman, An electromechanical finite element model for piezoelectric energy harvester plates, Journal of Sound and Vibration, 327(1) (2009) 9-25.
[4] A. Erturk, J. Hoffmann, D. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting, Applied Physics Letters, 94(25) (2009) 254102.
[5] X. Dai, Y. Wen, P. Li, J. Yang, G. Zhang, Modeling, characterization and fabrication of vibration energy harvester using Terfenol-D/PZT/Terfenol-D composite transducer, Sensors and Actuators A: Physical, 156(2) (2009) 350-358.
[6] K.H. Sun, Y.Y. Kim, Layout design optimization for magneto-electro-elastic laminate composites for maximized energy conversion under mechanical loading, Smart Materials and Structures, 19(5) (2010) 055008.
[7] A. Milazzo, C. Orlando, An equivalent single-layer approach for free vibration analysis of smart laminated thick composite plates, Smart Materials and Structures, 21(7) (2012) 075031.
[8] Z. Wu, R. Harne, K. Wang, Excitation-induced stability in a bistable Duffing oscillator: analysis and experiments, Journal of Computational and Nonlinear Dynamics, 10(1) (2015) 011016.
[9] M.M. El-Hebeary, M.H. Arafa, S.M. Megahed, Modeling and experimental verification of multi-modal vibration energy harvesting from plate structures, Sensors and Actuators A: Physical, 193 (2013) 35-47.
[10] S.C. Stanton, B.A. Owens, B.P. Mann, Harmonic balance analysis of the bistable piezoelectric inertial generator, Journal of Sound and Vibration, 331(15) (2012) 3617-3627.
[11] H. Talleb, Z. Ren, Finite element modeling of magnetoelectric laminate composites in considering nonlinear and load effects for energy harvesting, Journal of Alloys and Compounds, 615 (2014) 65-74.
[12] L.-L. Ke, Y.-S. Wang, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E: Low-dimensional Systems and Nanostructures, 63 (2014) 52-61.
[13] S. Razavi, A. Shooshtari, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures, 119 (2015) 377-384.
[14] M.M. Shirbani, M. Shishesaz, A. Hajnayeb, H.M. Sedighi, Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems, Physica E: Low-dimensional Systems and Nanostructures, 90 (2017) 158-169.
[15] H. Shorakaei, A. Shooshtari, Analytical solution and energy harvesting from nonlinear vibration of an asymmetric bimorph piezoelectric plate and optimizing the plate parameters by genetic algorithm, Journal of Intelligent Material Systems and Structures, (2017) 1045389X17730919.
[16] V. Birman, Plate structures, Springer Science & Business Media, Netherlands, 2011.
[17] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC press, 2004.
[18] C.-Y. Chia, Nonlinear analysis of plates, McGraw-Hill International Book Company, 1980.
[19] H.-S. Shen, Functionally graded materials: nonlinear analysis of plates and shells, CRC press, 2016.
[20] J.N. Reddy, Theory and analysis of elastic plates and shells, CRC press, 2006.
[21] M. Rafiee, X. He, K. Liew, Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates, Smart Materials and Structures, 23(6) (2014) 065001.
[22] A. Erturk, D.J. Inman, Piezoelectric energy harvesting, John Wiley & Sons, The Atrium, Southern Gate, Chichester, West Sussex, 2011.
[23] D.J. Griffiths, Introduction to electrodynamics, Prentice Hall, 93 (1999) 95.
[24] W.H. Hayt, J.A. Buck, Engineering electromagnetics, McGraw-Hill New York, 2001.
[25] T. Burton, Z. Rahman, On the multi-scale analysis of strongly non-linear forced oscillators, International Journal of Non-Linear Mechanics, 21(2) (1986) 135-146.
[26] A. Nayfeh, D. Mook, Nonlinear Oscillations, John Wiley and Sons, New York, (1979).
[27] H. Shorakaei, M. Vahdani, B. Imani, A. Gholami, Optimal cooperative path planning of unmanned aerial vehicles by a parallel genetic algorithm, Robotica, 34(04) (2016) 823-836.
[28] V. Azimirad, H. Shorakaei, Dual hierarchical genetic-optimal control: A new global optimal path planning method for robots, Journal of Manufacturing Systems, 33(1) (2014) 139-148.
[29] C.-X. Xue, E. Pan, On the longitudinal wave along a functionally graded magneto-electro-elastic rod, International Journal of Engineering Science, 62 (2013) 48-55.
AUT Journal of Mechanical Engineering
Volume 3, Issue 1
May 2019
Pages 63-76

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