Oscillators for Energy Harvesting

  • E. BlokhinaEmail author
  • D. Galayko


The aim of this chapter is to briefly explain fundamental concepts such as linear and nonlinear oscillators and transducers since they are required for understanding the energy harvesting principle. We discuss the model of free and harmonically driven linear and nonlinear oscillators. In particular, we show that the solution of a forced linear oscillator is a harmonic oscillation at the frequency of the external signal. We discuss the principles of nonlinear oscillators, resonance in nonlinear oscillator and multistability. In order to use an oscillator for the energy harvesting process, one requires a transducer, a device that takes power from one domain (for instance, the mechanical domain) and converts it to another domain (for instance, the electrical domain). In this chapter, we discuss the two most suitable transducers for micro- and nanoscale harvesting—piezoelectric and electrostatic transducers.


  1. 1.
    Adams, S. G., Bertsch, F. M., Shaw, K. A., & MacDonald, N. C. (1998). Independent tuning of linear and nonlinear stiffness coefficients [actuators]. Journal of Microelectromechanical Systems, 7(2), 172–180.CrossRefGoogle Scholar
  2. 2.
    Amri, M., Basset, P., Cottone, F., Galayko, D., Najar, F., & Bourouina, T. (2011). Novel nonlinear spring design for wideband vibration energy harvesters. In Proceedings of the power MEMS (pp. 15–18).Google Scholar
  3. 3.
    Andronov, A. A. (1987). Theory of oscillators (Vol. 4). Courier Dover Publications.Google Scholar
  4. 4.
    Beeby, S., Torah, R., Tudor, M., Glynne-Jones, P., O’Donnell, T., Saha, C., et al. (2007). A micro electromagnetic generator for vibration energy harvesting. Journal of Micromechanics and Microengineering, 17, 1257.CrossRefGoogle Scholar
  5. 5.
    Beeby, S. P., Tudor, M. J., & White, N. M. (2009). Energy harvesting vibration sources for microsystems applications. Measurement Science and Technology, 17, R175–R195.CrossRefGoogle Scholar
  6. 6.
    Benzi, R., Sutera, A., & Vulpiani, A. (1981). The mechanism of stochastic resonance. Journal of Physics A: Mathematical and General, 14(11), L453.MathSciNetCrossRefGoogle Scholar
  7. 7.
    DeMartini, B. E., Rhoads, J. F., Turner, K. L., Shaw, S. W., & Moehlis, J. (2007). Linear and nonlinear tuning of parametrically excited mems oscillators. Journal of Microelectromechanical Systems, 16(2), 310–318.CrossRefGoogle Scholar
  8. 8.
    Duffing, G. (1918). Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung. 41–42. R, Vieweg and Sohn.Google Scholar
  9. 9.
    Galchev, T., Aktakka, E. E., & Najafi, K. (2012). A piezoelectric parametric frequency increased generator for harvesting low-frequency vibrations. Journal of Microelectromechanical Systems, 21(6), 1311–1320.CrossRefGoogle Scholar
  10. 10.
    Gammaitoni, L., Neri, I., & Vocca, H. (2009). Nonlinear oscillators for vibration energy harvesting. Applied Physics Letters, 94, 164,102.Google Scholar
  11. 11.
    Guckenheimer, J., & Holmes, P. (1983). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (Vol. 42). New York: Springer.Google Scholar
  12. 12.
    Hairer, E., Nørsett, S. P., & Wanner, G. (1991). Solving ordinary differential equations (Vol. 2). Springer.Google Scholar
  13. 13.
    Holmes, P., & Rand, D. (1976). The bifurcations of Duffing’s equation: An application of catastrophe theory. Journal of Sound and Vibration, 44(2), 237–253.CrossRefzbMATHGoogle Scholar
  14. 14.
    Kaajakari, V. (2009). Practical MEMS: Design of microsystems, accelerometers, gyroscopes, RF MEMS, optical MEMS, and microfluidic systems. Las Vegas, NV: Small Gear Publishing.Google Scholar
  15. 15.
    Kuznetsov, A. P., Kuznetsov, S. P., & Ryskin, N. (2002). Nonlinear oscillations. Moscow: Fizmatlit.zbMATHGoogle Scholar
  16. 16.
    Li, H., Preidikman, S., Balachandran, B., & Mote, C, Jr. (2006). Nonlinear free and forced oscillations of piezoelectric microresonators. Journal of Micromechanics and Microengineering, 16(2), 356.CrossRefGoogle Scholar
  17. 17.
    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.Google Scholar
  18. 18.
    Mitcheson, P., Yeatman, E., Rao, G., Holmes, A., & Green, T. (2008). Energy harvesting from human and machine motion for wireless electronic devices. Proceedings of the IEEE, 96(9), 1457–1486.CrossRefGoogle Scholar
  19. 19.
    Nayfeh, A. (1993). Introduction to perturbation techniques. Wiley.Google Scholar
  20. 20.
    Nayfeh, A. H., & Balachandran, B. (2008). Applied nonlinear dynamics (Vol. 24). Wiley-VCH.Google Scholar
  21. 21.
    Nayfeh, A. H., & Mook, D. T. (2008). Nonlinear oscillations. Wiley.Google Scholar
  22. 22.
    Nayfeh, A. H., Younis, M. I., & Abdel-Rahman, E. M. (2005). Reduced-order models for mems applications. Nonlinear dynamics, 41(1–3), 211–236.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Nguyen, D., Halvorsen, E., Jensen, G., & Vogl, A. (2010). Fabrication and characterization of a wideband mems energy harvester utilizing nonlinear springs. Journal of Micromechanics and Microengineering, 20(12), 125,009.Google Scholar
  24. 24.
    Nguyen, S. D., & Halvorsen, E. (2011). Nonlinear springs for bandwidth-tolerant vibration energy harvesting. Journal of Microelectromechanical Systems, 20, 1225–1227.CrossRefGoogle Scholar
  25. 25.
    Nicolis, C. (1981). Solar variability and stochastic effects on climate. In Physics of Solar Variations (pp. 473–478). Springer.Google Scholar
  26. 26.
    Nicolis, C. (1982). Stochastic aspects of climatic transitions response to a periodic forcing. Tellus, 34(1), 1–9.MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pelesko, J. A., & Bernstein, D. H. (2002). Modeling MEMS and NEMS. CRC Press.Google Scholar
  28. 28.
    Rabinovich, M. I. (1989). Oscillations and waves: In linear and nonlinear systems (Vol. 50). Taylor and Francis.Google Scholar
  29. 29.
    Riley, K., Hobson, P., & Bence, S. (2006). Mathematical methods for physics and engineering: a comprehensive guide. Cambridge University Press.
  30. 30.
    Roundy, S., Wright, P., & Pister, K. (2002) Micro-electrostatic vibration-to-electricity converters. In Proceedings of 2002 ASME international mechanical engineering congress.Google Scholar
  31. 31.
    Senturia, S. D. (2001). Microsystem design (Vol. 3). Boston: Kluwer Academic Publishers.Google Scholar
  32. 32.
    Tang, K. T. (2007). Mathematical methods for engineers and scientists. Springer.Google Scholar
  33. 33.
    Tang, L., Yang, Y., & Soh, C. K. (2010). Toward broadband vibration-based energy harvesting. Journal of Intelligent Material Systems and Structures, 21(18), 1867–1897.CrossRefGoogle Scholar
  34. 34.
    Taylor, J. R. (2005). Classical mechanics. University Science Books.Google Scholar
  35. 35.
    Trubetskov, D. I., & Rozhnev, A. G. (2001). Linear oscillations and waves. Moscow: Fizmatlit.Google Scholar
  36. 36.
    Williams, C., & Yates, R. (1996). Analysis of a micro-electric generator for microsystems. Sensors and Actuators A, 52, 8–11.CrossRefGoogle Scholar
  37. 37.
    Zhu, D., Tudor, M. J., & Beeby, S. P. (2010). Strategies for increasing the operating frequency range of vibration energy harvesters: A review. Measurements and Science Technology, 21, 022,001.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University College DublinDublinIreland
  2. 2.UPMC—Sorbonne UniversitiesParisFrance

Personalised recommendations