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On the energy extraction from large amplitude vibrations of MEMS-based piezoelectric harvesters

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Abstract

As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and adding concentrated tip masses where both result in a sensitivity enhancement as well. Therefore, according to the amplitude and frequency of applied excitations and physical parameters of the harvester, large amplitude motions can occurr in these systems. In this study, nonlinear dynamics of a piezoelectric harvester under large amplitude vibrations is investigated. To that end first of all an accurate comprehensive fully coupled electromechanical nonlinear model is extracted through a constrained Hamilton’s variational principle. A semi-analytical approach implementing the perturbation method of multiple scales is used to solve the governing coupled nonlinear differential equations of the model and analyze the primary and superharmonic resonances. Results indicate that as excitation grows, the output power response curves are right bended leading to enhancement of the harvester bandwidth. At primary resonance a second-order harmonic of the excitation frequency is present in the output voltage as a consequence of both nonlinear curvature and inertia due to shortening effect. Furthermore, the existence of superharmonic resonances makes it possible to extract considerable amounts of power at fractions of natural frequency which is very beneficial in MEMS-based harvesters with generally high resonance frequencies.

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References

  1. Elfrink, R., Renaud, M., Kamel, T., De Nooijer, C., Jambunathan, M., Goedbloed, M., Hohlfeld, D., Matova, S., Pop, V., Caballero, L.: Vacuum-packaged piezoelectric vibration energy harvesters: damping contributions and autonomy for a wireless sensor system. J. Micromech. Microeng. 20(10), 104001 (2010)

    Article  Google Scholar 

  2. Yu, H., Zhou, J., Deng, L., Wen, Z.: A vibration-based mems piezoelectric energy harvester and power conditioning circuit. Sensors 14(2), 3323–3341 (2014)

    Article  Google Scholar 

  3. Miao, P., Mitcheson, P., Holmes, A., Yeatman, E., Green, T., Stark, B.: MEMS inertial power generators for biomedical applications. Microsyst. Technol. 12(10–11), 1079–1083 (2006)

    Article  Google Scholar 

  4. He, C., Arora, A., Kiziroglou, M.E., Yates, D.C., O’Hare, D., Yeatman, E.M.: MEMS energy harvesting powered wireless biometric sensor. In: Wearable and Implantable Body Sensor Networks, 2009. BSN 2009. Sixth International Workshop on 2009, pp. 207-212. IEEE

  5. Hande, A., Bridgelall, R., Bhatia, D.: Energy harvesting for active RF sensors and ID tags. In: Priya, S., Inman, D. J. (Eds.) Energy Harvesting Technologies. pp. 459-492. Springer, Berlin (2009)

  6. Kaya, T., Koser, H.: A new batteryless active RFID system: smart RFID. In: RFID Eurasia, 2007 1st Annual 2007, pp. 1-4. IEEE

  7. Roundy, S., Wright, P., Rabaey, J.: Energy Scavenging for Wireless Sensor Networks: With Special Focus on Vibrations. Kluwer Academic Publishers, Norwell (2004)

    Book  Google Scholar 

  8. Wang, P., Tanaka, K., Sugiyama, S., Dai, X., Zhao, X., Liu, J.: A micro electromagnetic low level vibration energy harvester based on MEMS technology. Microsyst. Technol. 15(6), 941–951 (2009)

    Article  Google Scholar 

  9. Williams, C., Shearwood, C., Harradine, M., Mellor, P., Birch, T., Yates, R.: Development of an electromagnetic micro-generator. In: Circuits, Devices and Systems, IEE Proceedings- 2001, pp. 337–342. IET

  10. Mitcheson, P.D., Miao, P., Stark, B.H., Yeatman, E., Holmes, A., Green, T.: MEMS electrostatic micropower generator for low frequency operation. Sens. Actuators A 115(2), 523–529 (2004)

    Article  Google Scholar 

  11. Sheu, G.-J., Yang, S.-M., Lee, T.: Development of a low frequency electrostatic comb-drive energy harvester compatible to SoC design by CMOS process. Sens. Actuators A 167(1), 70–76 (2011)

    Article  Google Scholar 

  12. Liu, J.-Q., Fang, H.-B., Xu, Z.-Y., Mao, X.-H., Shen, X.-C., Chen, D., Liao, H., Cai, B.-C.: A MEMS-based piezoelectric power generator array for vibration energy harvesting. Microelectron. J. 39(5), 802–806 (2008)

    Article  Google Scholar 

  13. Chung, G.-S., Lee, B.-C.: Fabrication and characterization of vibration-driven AlN piezoelectric micropower generator compatible with complementary metal-oxide semiconductor process. J. Intell. Mater. Syst. Struct. (2014). doi:10.1177/1045389X14546649

    Google Scholar 

  14. Sue, C.-Y., Tsai, N.-C.: Human powered MEMS-based energy harvest devices. Appl. Energy 93, 390–403 (2012)

    Article  Google Scholar 

  15. Roundy, S., Wright, P.K.: A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct. 13(5), 1131 (2004)

    Article  Google Scholar 

  16. Benasciutti, D., Moro, L., Zelenika, S., Brusa, E.: Vibration energy scavenging via piezoelectric bimorphs of optimized shapes. Microsyst. Technol. 16(5), 657–668 (2010)

    Article  Google Scholar 

  17. Shen, D., Park, J.-H., Ajitsaria, J., Choe, S.-Y., Wikle III, H.C., Kim, D.-J.: The design, fabrication and evaluation of a MEMS PZT cantilever with an integrated Si proof mass for vibration energy harvesting. J. Micromech. Microeng. 18(5), 055017 (2008)

    Article  Google Scholar 

  18. Aktakka, E., Kim, H., Najafi, K.: 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 2009, pp. 849–852. IEEE

  19. Elfrink, R., Kamel, T., Goedbloed, M., Matova, S., Hohlfeld, D., Van Andel, Y., Van Schaijk, R.: Vibration energy harvesting with aluminum nitride-based piezoelectric devices. J. Micromech. Microeng. 19(9), 094005 (2009)

    Article  Google Scholar 

  20. Jeon, Y., Sood, R., Jeong, J.-H., Kim, S.-G.: MEMS power generator with transverse mode thin film PZT. Sens. Actuators A 122(1), 16–22 (2005)

    Article  Google Scholar 

  21. Lee, B., Lin, S., Wu, W.: Fabrication and evaluation of a MEMS piezoelectric bimorph generator for vibration energy harvesting. J. Mech. 26(04), 493–499 (2010)

    Article  Google Scholar 

  22. Lu, F., Lee, H., Lim, S.: Modeling and analysis of micro piezoelectric power generators for micro-electromechanical-systems applications. Smart Mater. Struct. 13(1), 57 (2004)

    Article  Google Scholar 

  23. Lesieutre, G.A., Ottman, G.K., Hofmann, H.F.: Damping as a result of piezoelectric energy harvesting. J. Sound Vib. 269(3), 991–1001 (2004)

    Article  Google Scholar 

  24. Jiang, S., Li, X., Guo, S., Hu, Y., Yang, J., Jiang, Q.: Performance of a piezoelectric bimorph for scavenging vibration energy. Smart Mater. Struct. 14(4), 769 (2005)

    Article  Google Scholar 

  25. Chen, S.-N., Wang, G.-J., Chien, M.-C.: Analytical modeling of piezoelectric vibration-induced micro power generator. Mechatronics 16(7), 379–387 (2006)

    Article  Google Scholar 

  26. Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vib. Acoust. 130(4), 041002 (2008)

    Article  Google Scholar 

  27. Junior, C.D.M., Erturk, A., Inman, D.J.: An electromechanical finite element model for piezoelectric energy harvester plates. J. Sound Vib. 327(1), 9–25 (2009)

    Article  Google Scholar 

  28. Andosca, R., McDonald, T.G., Genova, V., Rosenberg, S., Keating, J., Benedixen, C., Wu, J.: Experimental and theoretical studies on MEMS piezoelectric vibrational energy harvesters with mass loading. Sens. Actuators A 178, 76–87 (2012)

    Article  Google Scholar 

  29. Lumentut, M., Howard, I.: Intrinsic electromechanical dynamic equations for piezoelectric power harvesters. Acta Mech. bf 228(2), 631–650 (2017) doi:10.1007/s00707-016-1726-y

  30. Pasharavesh, A., Ahmadian, M.T., Zohoor, H.: Coupled electromechanical analysis of MEMS-based energy harvesters integrated with nonlinear power extraction circuits. Microsyst. Technol, 1–18 (2016). doi:10.1007/s00542-016-3024-y

  31. Krommer, M., Irschik, H.: An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics. Acta Mech. 154(1–4), 141–158 (2002)

    Article  MATH  Google Scholar 

  32. Erturk, A.: Assumed-modes modeling of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh, and Timoshenko models with axial deformations. Comput. Struct. 106, 214–227 (2012)

    Article  Google Scholar 

  33. Chee, C.Y., Tong, L., Steven, G.P.: A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. J. Intell. Mater. Syst. Struct. 9(1), 3–19 (1998)

    Article  Google Scholar 

  34. Kapuria, S., Kumari, P., Nath, J.: Efficient modeling of smart piezoelectric composite laminates: a review. Acta Mech. 214(1–2), 31–48 (2010)

    Article  MATH  Google Scholar 

  35. Yang, B., Liu, H., Liu, J., Lee, C.: Micro and Nano Energy Harvesting Technologies. Artech House, Norwood (2014)

    Google Scholar 

  36. Masana, R., Daqaq, M.F.: Relative performance of a vibratory energy harvester in mono-and bi-stable potentials. J. Sound Vib. 330(24), 6036–6052 (2011)

    Article  Google Scholar 

  37. Daqaq, M.F.: Response of uni-modal duffing-type harvesters to random forced excitations. J. Sound Vib. 329(18), 3621–3631 (2010)

    Article  Google Scholar 

  38. Panyam, M., Daqaq, M.F.: A comparative performance analysis of electrically optimized nonlinear energy harvesters. J. Intell. Mater. Syst. Struct. (2015). doi:10.1177/1045389X15573344

    Google Scholar 

  39. Ferrari, M., Ferrari, V., Guizzetti, M., Andò, B., Baglio, S., Trigona, C.: Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters. Sens. Actuators A 162(2), 425–431 (2010)

    Article  Google Scholar 

  40. Cottone, F., Vocca, H., Gammaitoni, L.: Nonlinear energy harvesting. Phys. Rev. Lett. 102(8), 080601 (2009)

    Article  Google Scholar 

  41. Jia, Y., Yan, J., Soga, K., Seshia, A.A.: A parametrically excited vibration energy harvester. J. Intell. Mater. Syst. Struct. (2013). doi:10.1177/1045389X13491637

    Google Scholar 

  42. Mahmoodi, S.N., Afshari, M., Jalili, N.: Nonlinear vibrations of piezoelectric microcantilevers for biologically-induced surface stress sensing. Commun. Nonlinear Sci. Numer. Simul. 13(9), 1964–1977 (2008)

    Article  Google Scholar 

  43. Daqaq, M.F., Stabler, C., Qaroush, Y., Seuaciuc-Osório, T.: Investigation of power harvesting via parametric excitations. J. Intell. Mater. Syst. Struct. 20(5), 545–557 (2009)

    Article  Google Scholar 

  44. Lin, C.-H., Muliana, A.: Micromechanics models for the effective nonlinear electro-mechanical responses of piezoelectric composites. Acta Mech. 224(7), 1471–1492 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Choi, S.-B.: Vibration control of a smart beam structure subjected to actuator uncertainty: experimental verification. Acta Mech. 181(1–2), 19–30 (2006)

    Article  MATH  Google Scholar 

  46. Irschik, H., Gerstmayr, J.: A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams. Acta Mech. 206(1–2), 1–21 (2009)

    Article  MATH  Google Scholar 

  47. Irschik, H., Gerstmayr, J.: A continuum-mechanics interpretation of Reissner’s non-linear shear-deformable beam theory. Math. Comput. Model. Dyn. Syst. 17(1), 19–29 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  48. Arafat, H.N.: Nonlinear response of cantilever beams. Doctoral dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia (1999)

  49. Malatkar, P.: Nonlinear vibrations of cantilever beams and plates. Doctoral dissertation, Virginia Tech, Blacksburg, Virginia (2003)

  50. Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics. Wiley, Hoboken (2008)

    MATH  Google Scholar 

  51. Yang, J.: An Introduction to the Theory of Piezoelectricity, vol. 9. Springer, Berlin (2005)

    MATH  Google Scholar 

  52. Rao, S.S.: Vibration of Continuous Systems. Wiley, Hoboken (2007)

    Google Scholar 

  53. Zamanian, M., Khadem, S.: Nonlinear vibration of an electrically actuated microresonator tuned by combined DC piezoelectric and electric actuations. Smart Mater. Struct. 19(1), 015012 (2009)

    Article  Google Scholar 

  54. Defosseux, M., Allain, M., Defay, E., Basrour, S.: Highly efficient piezoelectric micro harvester for low level of acceleration fabricated with a CMOS compatible process. Sens. Actuators A 188, 489–494 (2012)

    Article  Google Scholar 

  55. Ottman, G.K., Hofmann, H.F., Bhatt, A.C., Lesieutre, G.: Adaptive piezoelectric energy harvesting circuit for wireless remote power supply. IEEE Trans. Power Electron. 17(5), 669–676 (2002)

    Article  Google Scholar 

  56. Roundy, S., Wright, P.K., Rabaey, J.: A study of low level vibrations as a power source for wireless sensor nodes. Comput. Commun. 26(11), 1131–1144 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran

    Abdolreza Pasharavesh, M. T. Ahmadian & H. Zohoor

  2. Center of Excellence in Design, Robotics and Automation, Sharif University of Technology, Tehran, Iran

    M. T. Ahmadian

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  1. Abdolreza Pasharavesh
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  2. M. T. Ahmadian
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  3. H. Zohoor
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Correspondence to M. T. Ahmadian.

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Pasharavesh, A., Ahmadian, M.T. & Zohoor, H. On the energy extraction from large amplitude vibrations of MEMS-based piezoelectric harvesters. Acta Mech 228, 3445–3468 (2017). https://doi.org/10.1007/s00707-017-1864-x

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