Analytical and numerical simulations of energy harvesting using MEMS devices operating in nonlinear regime

  • Abdolreza PasharaveshEmail author
  • Mohammad Taghi Ahmadian
Regular Article
Part of the following topical collections:
  1. Topical issue: The Physics of Micro-Energy Use and Transformation


While macro-scale piezoelectric generators require base excitations with moderately large amplitudes to transit from the linear regime of vibration to the nonlinear one, for a MEMS harvester due to its small dimensions, this transition can occur at oscillatory base motions even smaller than a few microns, which necessitates the nonlinear analysis of MEMS harvesting devices in most environments. In this paper the coupled electromechanical behavior of a typical MEMS-based piezoelectric harvester in the nonlinear regime is investigated. Lagrange’s equations are used in accordance to the assumed mode method to extract the coupled nonlinear equations of motion governing the lateral deflection and output voltage. An analytical solution to the derived equations is performed employing the perturbation method of multiple scales providing the nonlinear frequency responses of the output power. Results indicate that although the effect of nonlinear inertia increases due to utilizing large tip masses in these harvesters, nonlinear curvature is still the dominant effect leading to hardening behavior of the response. The comparison of the responses of the nonlinear and linear devices shows a considerable enhancement of the frequency bandwidth in the nonlinear regime. Also a nonlinear coupled electromechanical FE simulation of the harvester is conducted using the ABAQUS software where a very good agreement is observed between the results of this simulation with both analytical and numerical solutions of the governing equations.


  1. 1.
    M.T. Dunham, M.T. Barako, S. LeBlanc, M. Asheghi, B. Chen, K.E. Goodson, Energy 93, 2006 2015 Google Scholar
  2. 2.
    W. Yang, K. Chua, J. Pan, D. Jiang, H. An, Energy Convers. Manag. 78, 81 (2014) Google Scholar
  3. 3.
    A.R.M. Siddique, S. Mahmud, B. Van Heyst, Energy Convers. Manag. 106, 728 (2015) Google Scholar
  4. 4.
    G.J. Sheu, S.M. Yang, T. Lee, Sens. Actuators A: Phys. 167, 70 (2011) CrossRefGoogle Scholar
  5. 5.
    P. Wang, K. Tanaka, S. Sugiyama, X. Dai, X. Zhao, J. Liu, Microsyst. Technol. 15, 941 (2009) CrossRefGoogle Scholar
  6. 6.
    G.S. Chung, B.C. Lee, J. Intell. Material Syst. Struct. 26, 1971 (2015) Google Scholar
  7. 7.
    P. Miao, P. Mitcheson, A. Holmes, E. Yeatman, T. Green, B. Stark, Microsyst Technol. 12, 1079 (2006) CrossRefGoogle Scholar
  8. 8.
    C. He, A. Arora, M.E. Kiziroglou, D.C. Yates, D. O’Hare, E.M. Yeatman, MEMS energy harvesting powered wireless biometric sensor, in Wearable and Implantable Body Sensor Networks, 2009. BSN 2009. Sixth International Workshop on IEEE (2009), pp. 207–212 Google Scholar
  9. 9.
    R. Elfrink et al., J. Micromech. Microeng. 20, 104001 (2010) CrossRefGoogle Scholar
  10. 10.
    H. Yu, J. Zhou, L. Deng, Z. Wen, Sensors 14, 3323 (2014) CrossRefGoogle Scholar
  11. 11.
    A. Hande, R. Bridgelall, D. Bhatia, in Energy Harvesting Technologies (Springer, 2009), pp. 459–492 Google Scholar
  12. 12.
    C. Bowen, M. Arafa, Adv. Energy Mater. 5, 1401787 (2015) CrossRefGoogle Scholar
  13. 13.
    C. Williams, C. Shearwood, M. Harradine, P. Mellor, T. Birch, R. Yates, IEE Proc. Circ. Dev. Syst. 148, 337 (2001) CrossRefGoogle Scholar
  14. 14.
    P.D. Mitcheson, P. Miao, B.H. Stark, E. Yeatman, A. Holmes, T. Green, Sens. Actuators A Phys. 115, 523 (2004) CrossRefGoogle Scholar
  15. 15.
    C.Y. Sue, N.C. Tsai, Appl. Energy 93, 390 (2012) Google Scholar
  16. 16.
    Y. Jeon, R. Sood, J.H. Jeong, S.G. Kim, Sens. Actuators A Phys. 122, 16 (2005) CrossRefGoogle Scholar
  17. 17.
    D. Shen, J.H. Park, J. Ajitsaria, S.Y. Choe, H.C. Wikle III, D.J. Kim, J. Micromech. Microeng. 18, 055017 (2008) CrossRefGoogle Scholar
  18. 18.
    E. Aktakka, H. Kim, K. Najafi, Wafer level fabrication of high performance MEMS using bonded and thinned bulk piezoelectric substrates, in Solid-State Sensors, Actuators and Microsystems Conference, 2009. TRANSDUCERS 2009. International IEEE, 2009 (2009), pp. 849–852 Google Scholar
  19. 19.
    A. Lei, R. Xu, A. Thyssen, A.C. Stoot, T.L. Christiansen, K. Hansen, R. Lou-Moeller, E.V. Thomsen, K. Birkelund, MEMS-based thick film PZT vibrational energy harvester, in Micro electro mechanical systems (MEMS), 2011 IEEE 24th international conference on IEEE, 2011 (2011), pp. 125–128 Google Scholar
  20. 20.
    R. Elfrink, T. Kamel, M. Goedbloed, S. Matova, D. Hohlfeld, Y. Van Andel, R. Van Schaijk, J. Micromech. Microeng. 19, 094005 (2009) CrossRefGoogle Scholar
  21. 21.
    B. Yang, H. Liu, J. Liu, C. Lee, Micro and Nano Energy Harvesting Technologies (Artech House, 2014) Google Scholar
  22. 22.
    P.L. Green, E. Papatheou, N.D. Sims, J. Intell. MaterialSyst. Struct. 24, 1494 (2013) Google Scholar
  23. 23.
    B. Mann, N. Sims, J. Sound Vib. 319, 515 (2009) CrossRefGoogle Scholar
  24. 24.
    D.A. Barton, S.G. Burrow, L.R. Clare, J. Vib. Acoustics 132, 021009 (2010) Google Scholar
  25. 25.
    D.D. Quinn, A.L. Triplett, L.A. Bergman, A.F. Vakakis, J. Vib. Acoustics 133, 011001 (2011) Google Scholar
  26. 26.
    S. Roundy, P.K. Wright, J. Rabaey, Comput. Commun. 26, 1131 (2003) CrossRefGoogle Scholar
  27. 27.
    F. Lu, H. Lee, S. Lim, Smart Mater. Struct. 13, 57 (2003) CrossRefGoogle Scholar
  28. 28.
    S.N. Chen, G.J. Wang, M.C. Chien, Mechatronics 16, 379 (2006) CrossRefGoogle Scholar
  29. 29.
    F. Cottone, H. Vocca, L. Gammaitoni, Phys. Rev. Lett. 102, 080601 (2009) CrossRefGoogle Scholar
  30. 30.
    A. Erturk, D. Inman, J. Sound Vib. 330, 2339 (2011) CrossRefGoogle Scholar
  31. 31.
    M. Ferrari, V. Ferrari, M. Guizzetti, B. Andò, S. Baglio, C. Trigona, Sens Actuators A: Phys. 162, 425 (2010) CrossRefGoogle Scholar
  32. 32.
    Y. Hu, H. Xue, J. Yang, Q. Jiang, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53, 1387 (2006) CrossRefGoogle Scholar
  33. 33.
    A. Pasharavesh, M. Ahmadian, H. Zohoor, Int. J. Mech. Mater. Des. 13, 499 (2017) CrossRefGoogle Scholar
  34. 34.
    Y. Hu, T. Hu, Q. Jiang, Acta Mechanica Solida Sinica 20, 296 (2007) CrossRefGoogle Scholar
  35. 35.
    A. Pasharavesh, M. Ahmadian, H. Zohoor, Microsyst. Technol. 23, 2403 (2017) CrossRefGoogle Scholar
  36. 36.
    A. Pasharavesh, M. Ahmadian, Appl. Math. Model. 41, 121 (2017) MathSciNetCrossRefGoogle Scholar
  37. 37.
    S.N. Mahmoodi, M. Afshari, N. Jalili, Commun. onlinear Sci. Numer. Simul. 13, 1964 2008 Google Scholar
  38. 38.
    J. Yang, in An introduction to the theory of piezoelectricity (Springer Science & Business Media, 2004), Vol. 9 Google Scholar
  39. 39.
    S.S. Rao, Vibration of continuous systems (John Wiley & Sons, 2007) Google Scholar
  40. 40.
    A.H. Nayfeh, D.T. Mook, Nonlinear oscillations (John Wiley & Sons, 2008) Google Scholar
  41. 41.
    M. Staworko, T. Uhl, Mechanics/AGH University of Science and Technology 27, 161 (2008) Google Scholar
  42. 42.
    J. Park, S. Lee, B.M. Kwak, J. Mech. Sci. Technol. 26, 137 (2012) CrossRefGoogle Scholar
  43. 43.
    L. Zhang, Analytical modeling and design optimization of piezoelectric bimorph energy harvester (The University of Alabama, 2010) Google Scholar
  44. 44.
    L.H. Tang, Y.W. Yang, System-Level Modeling of Piezoelectric Energy Harvesters, in Advanced Materials Research (Trans. Tech. Publ., 2009), Vol. 79, pp. 103–106 CrossRefGoogle Scholar
  45. 45.
    R. O’Keeffe, N. Jackson, F. Waldron, M. O’Niell, K. McCarthy, A. Mathewson, Investigation into modelling power output for MEMS energy harvesting devices using COMSOL Multiphysics R, in Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2013 14th International Conference on IEEE, 2013 (2013), pp. 1–6 Google Scholar
  46. 46.
    E. Varadarajan, M. Bhanusri, Design and simulation of unimorph piezoelectric energy harvesting system, in COMSOL Conference in Bangalore (2013), pp. 17–18 Google Scholar
  47. 47.
    G.K. Ottman, H.F. Hofmann, A.C. Bhatt, G.A. Lesieutre, IEEE Trans. Power Electron. 17, 669 (2002) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Abdolreza Pasharavesh
    • 1
    • 2
    Email author
  • Mohammad Taghi Ahmadian
    • 1
    • 2
  1. 1.Mechanical Engineering Department, Sharif University of TechnologyTehranIran
  2. 2.Center of Excellence in Design, Robotics and Automation, Sharif University of TechnologyTehranIran

Personalised recommendations