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2016 | OriginalPaper | Chapter

9. Analysis and Modelling of Nonlinearties in Vibration Energy Harvesters

Authors : Peter Harte, Dimitri Galayko, Orla Feely, Elena Blokhina

Published in: Nonlinearity in Energy Harvesting Systems

Publisher: Springer International Publishing

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Abstract

This chapter introduces the reader to a nonlinear mathematical model of an electrostatic vibration energy harvester and how it is developed. Semi-analytical techniques for analysing the dynamical behaviour and stability of the systems are introduced with particular emphasis on the harmonic balance method, the multiple scales method and the mechanical impedance method. These methods are compared and different ways to visualise and interpret the results of both numerical integration of the mathematical model, and the semi-analytical techniques are presented. Although the chapter is primarily focused on a gap closing eVEH operating in the constant charge mode, the material studied gives the reader the necessary tools to analyse and model any eVEH with nonlinearity present in its system.

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Literature
1.
go back to reference Meninger, S., Mur-Miranda, J., Amirtharajah, R., Chandrakasan, A., & Lang, J. (2001). Vibration-to-electric energy conversion. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 9(1), 64–76.CrossRef Meninger, S., Mur-Miranda, J., Amirtharajah, R., Chandrakasan, A., & Lang, J. (2001). Vibration-to-electric energy conversion. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 9(1), 64–76.CrossRef
2.
go back to reference Galayko, D., & Basset, P. (2011). A general analytical tool for the design of vibration energy harvesters (VEHs) based on the mechanical impedance concept. IEEE Transactions on Circuits and Systems I, 99, 299–311.MathSciNetCrossRef Galayko, D., & Basset, P. (2011). A general analytical tool for the design of vibration energy harvesters (VEHs) based on the mechanical impedance concept. IEEE Transactions on Circuits and Systems I, 99, 299–311.MathSciNetCrossRef
3.
go back to reference Juillard, J. (2014). A comparative study of reduced-order modeling techniques for nonlinear mems beams. In DTIP 2014, pp. 261–265. Juillard, J. (2014). A comparative study of reduced-order modeling techniques for nonlinear mems beams. In DTIP 2014, pp. 261–265.
4.
go back to reference Nayfeh, A. H., & Balachandran, B. (2008). Applied nonlinear dynamics (Vol. 24). Wiley-VCH. Nayfeh, A. H., & Balachandran, B. (2008). Applied nonlinear dynamics (Vol. 24). Wiley-VCH.
5.
go back to reference Nguyen, C. H., & Halvorsen, E. (2014). Harmonic-balance analysis of nonlinear energy harvester models In IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2608–2611. Nguyen, C. H., & Halvorsen, E. (2014). Harmonic-balance analysis of nonlinear energy harvester models In IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2608–2611.
6.
go back to reference Nayfeh, A. (1993). Introduction to perturbation techniques. Wiley. Nayfeh, A. (1993). Introduction to perturbation techniques. Wiley.
7.
go back to reference Blokhina, E., Galayko, D., Basset, P., & Feely, O. (2013). Steady-state oscillations in resonant electrostatic vibration energy harvesters. IEEE Transactions on Circuits and Systems I, 60, 875–884.MathSciNetCrossRef Blokhina, E., Galayko, D., Basset, P., & Feely, O. (2013). Steady-state oscillations in resonant electrostatic vibration energy harvesters. IEEE Transactions on Circuits and Systems I, 60, 875–884.MathSciNetCrossRef
8.
go back to reference Blokhina, E., Fournier-Prunaret, D., Harte, P., Galayko, D., & Feely, O. (2013). Combined mechanical and circuit nonlinearities in electrostatic vibration energy harvesters. In Proceedings of the IEEE International Symposium on Circuits and Systems 2013, Beijing, China, 19–23 May 2013, 2013. Blokhina, E., Fournier-Prunaret, D., Harte, P., Galayko, D., & Feely, O. (2013). Combined mechanical and circuit nonlinearities in electrostatic vibration energy harvesters. In Proceedings of the IEEE International Symposium on Circuits and Systems 2013, Beijing, China, 19–23 May 2013, 2013.
9.
go back to reference Blokhina, E., Galayko, D., Harte, P., Basset, P., & Feely, O. (2012). Limit on converted power in resonant electrostatic vibration energy harvesters. Applied Physics Letters, 101, 173904.CrossRef Blokhina, E., Galayko, D., Harte, P., Basset, P., & Feely, O. (2012). Limit on converted power in resonant electrostatic vibration energy harvesters. Applied Physics Letters, 101, 173904.CrossRef
10.
go back to reference Yen, B. C., & Lang, J. H. (2006). A variable-capacitance vibration-to-electric energy harvester. IEEE Transactions on Circuits and Systems I, 53, 288–295.CrossRef Yen, B. C., & Lang, J. H. (2006). A variable-capacitance vibration-to-electric energy harvester. IEEE Transactions on Circuits and Systems I, 53, 288–295.CrossRef
11.
go back to reference Shu, Y., & Lien, I. (2006). Efficiency of energy conversion for a piezoelectric power harvesting system. Journal of Micromechanics and Microengineering, 16, 2429.CrossRef Shu, Y., & Lien, I. (2006). Efficiency of energy conversion for a piezoelectric power harvesting system. Journal of Micromechanics and Microengineering, 16, 2429.CrossRef
12.
go back to reference Levitan, E. (1960). Forced oscillation of a spring-mass system having combined coulomb and viscous damping. The Journal of the Acoustical Society of America, 32, 1265.MathSciNetCrossRef Levitan, E. (1960). Forced oscillation of a spring-mass system having combined coulomb and viscous damping. The Journal of the Acoustical Society of America, 32, 1265.MathSciNetCrossRef
13.
go back to reference Harte, P., Blokhina, E., Feely, O., Fournier-Prunaret, D., & Galayko, D. (2014). Electrostatic vibration energy harvesters with linear and nonlinear resonators. International Journal of Bifurcation and Chaos, 24(11), 1430030.CrossRefMATH Harte, P., Blokhina, E., Feely, O., Fournier-Prunaret, D., & Galayko, D. (2014). Electrostatic vibration energy harvesters with linear and nonlinear resonators. International Journal of Bifurcation and Chaos, 24(11), 1430030.CrossRefMATH
14.
go back to reference Hilborn, R. C. (2000). Chaos and nonlinear dynamics: An introduction for scientists and engineers. Oxford: Oxford University Press. www.summon.com. Hilborn, R. C. (2000). Chaos and nonlinear dynamics: An introduction for scientists and engineers. Oxford: Oxford University Press. www.​summon.​com.
15.
go back to reference Blokhina, E., Galayko, D., Wade, R., Basset, P., & Feely, O. (2012). Bifurcations and chaos in electrostatic vibration energy harvesters. In Proceedings of the IEEE International Symposium on Circuits and Systems 2012, Seoul, Korea, 20–24 May 2012, 2012, pp. 397–400. Blokhina, E., Galayko, D., Wade, R., Basset, P., & Feely, O. (2012). Bifurcations and chaos in electrostatic vibration energy harvesters. In Proceedings of the IEEE International Symposium on Circuits and Systems 2012, Seoul, Korea, 20–24 May 2012, 2012, pp. 397–400.
16.
go back to reference Galayko, D., Guillemet, R., Dudka, A., Basset, P. (2011). Comprehensive dynamic and stability analysis of electrostatic vibration energy harvester (E-VEH). In Proceedings of International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2011, pp. 2382–2385. Galayko, D., Guillemet, R., Dudka, A., Basset, P. (2011). Comprehensive dynamic and stability analysis of electrostatic vibration energy harvester (E-VEH). In Proceedings of International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2011, pp. 2382–2385.
17.
go back to reference Giaouris, D., Banerjee, S., Zahawi, B., & Pickert, V. (2008). Stability analysis of the continuous-conduction-mode buck converter via Filippov’s method. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(4), 1084–1096.MathSciNetCrossRef Giaouris, D., Banerjee, S., Zahawi, B., & Pickert, V. (2008). Stability analysis of the continuous-conduction-mode buck converter via Filippov’s method. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(4), 1084–1096.MathSciNetCrossRef
18.
go back to reference Filippov, A. (1998). Differential equations with discontinuous righthand sides: Control systems. Springer. Filippov, A. (1998). Differential equations with discontinuous righthand sides: Control systems. Springer.
19.
go back to reference Utkin, V. (1992). Sliding modes in control optimization. Springer. Utkin, V. (1992). Sliding modes in control optimization. Springer.
20.
go back to reference Leine, R., & Nijmeijer, H. (2006). Dynamics and bifurcations of non-smooth mechanical systems. Springer. Leine, R., & Nijmeijer, H. (2006). Dynamics and bifurcations of non-smooth mechanical systems. Springer.
Metadata
Title
Analysis and Modelling of Nonlinearties in Vibration Energy Harvesters
Authors
Peter Harte
Dimitri Galayko
Orla Feely
Elena Blokhina
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-20355-3_9