Acta Mechanica Sinica

, Volume 34, Issue 3, pp 561–577 | Cite as

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

Research Paper
  • 129 Downloads

Abstract

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler–Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton’s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency–response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency–response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Keywords

Parametric and external excitations Nonlinear distributed parameter model Nonlinear dynamic response Energy harvesting Harmonic balance method 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant 11172087).

References

  1. 1.
    Cook-Chennault, K.A., Thambi, N., Sastry, A.M.: Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct. 17, 043001 (2008)CrossRefGoogle Scholar
  2. 2.
    Anton, S.R., Sodano, H.A.: A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct. 16, R1–R21 (2007)CrossRefGoogle Scholar
  3. 3.
    Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. ASME J. Vib. Acoust. 130, 041002 (2008)CrossRefGoogle Scholar
  4. 4.
    Muralt, P.: Ferroelectric thin films for micro-sensors and actuators: a review. J. Micromech. Microeng. 10, 136–146 (2000)CrossRefGoogle Scholar
  5. 5.
    Caliò, R., Rongala, U.B., Camboni, D., et al.: Piezoelectric energy harvesting solutions. Sensors 14, 4755–90 (2014)CrossRefGoogle Scholar
  6. 6.
    Beeby, S.P., Tudor, M.J., White, N.M.: Energy harvesting vibration sources for microsystems applications. Meas. Sci. Technol. 17, R175–R195 (2006)CrossRefGoogle Scholar
  7. 7.
    Priya, S.: Advances in energy harvesting using low profile piezoelectric transducers. J. Electroceram. 19, 167–184 (2007)CrossRefGoogle Scholar
  8. 8.
    Sodano, H.A., Inman, D.J., Park, G.: A review of power harvesting from vibration using piezoelectric materials. Shock Vib. Dig. 36, 197–205 (2004)CrossRefGoogle Scholar
  9. 9.
    Kim, M., Hoegen, M., Dugundji, J., et al.: Modeling and experimental verification of proof mass effects on vibration energy harvester performance. Smart Mater. Struct. 19, 045023 (2010)CrossRefGoogle Scholar
  10. 10.
    Sodano, H.A., Park, G., Inman, D.J.: Estimation of electric charge output for piezoelectric energy harvesting. Strain 40, 49–58 (2004)CrossRefGoogle Scholar
  11. 11.
    Rafique, S., Bonello, P.: Experimental validation of a distributed parameter piezoelectric bimorph cantilever energy harvester. Smart Mater. Struct. 19, 094008 (2010)CrossRefGoogle Scholar
  12. 12.
    Tang, L.P., Wang, J.G.: Size effect of tip mass on performance of cantilevered piezoelectric energy harvester with a dynamic magnifier. Acta Mech. 228, 3997–4015 (2017)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Daqaq, M.F., Masana, R., Erturk, A., et al.: On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. ASME Appl. Mech. Rev. 66, 040801 (2014)CrossRefGoogle Scholar
  14. 14.
    Mahmoodi, S.N., Daqaq, M.F., Jalili, N.: On the nonlinear-flexural response of piezoelectrically driven microcantilever sensors. Sens. Actuators A Phys. 153, 171–179 (2009)CrossRefGoogle Scholar
  15. 15.
    Mahmoodi, S.N., Jalili, N.: Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers. Int. J. Non-Linear Mech. 42, 577–587 (2007)CrossRefGoogle Scholar
  16. 16.
    Mahmoodi, S.N., Jalili, N., Ahmadian, M.: Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers. Nonlinear Dyn. 59, 397–409 (2010)CrossRefMATHGoogle Scholar
  17. 17.
    Stanton, S.C., Erturk, A., Mann, B.P., et al.: Nonlinear piezoelectricity in electroelastic energy harvesters: modeling and experimental identification. J. Appl. Phys. 108, 074903 (2010)CrossRefGoogle Scholar
  18. 18.
    Abdelkefi, A., Nayfeh, A.H., Hajj, M.R.: Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation. Nonlinear Dyn. 67, 1221–1232 (2012)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Triplett, A., Quinn, D.D.: The effect of non-linear piezoelectric coupling on vibration-based energy harvesting. J. Intell. Mater. Syst. Struct. 20, 1959–1967 (2009)CrossRefGoogle Scholar
  20. 20.
    Neiss, S., Goldschmidtboeing, F., Kroener, M., et al.: Analytical model for nonlinear piezoelectric energy harvesting devices. Smart Mater. Struct. 23, 105031 (2014)CrossRefGoogle Scholar
  21. 21.
    Mousa, A.A., Sayed, M., Eldesoky, I.M., et al.: Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations. Int. J. Dyn. Control 2, 494–508 (2014)CrossRefGoogle Scholar
  22. 22.
    Mahmoudi, S., Kacem, N., Bouhaddi, N.: Enhancement of the performance of a hybrid nonlinear vibration energy harvester based on piezoelectric and electromagnetic transductions. Smart Mater. Struct. 23, 075024 (2014)CrossRefGoogle Scholar
  23. 23.
    Friswell, M.I., Ali, S.F., Bilgen, O., et al.: Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass. J. Intell. Mater. Syst. Struct. 23, 1505–1521 (2012)CrossRefGoogle Scholar
  24. 24.
    Chen, L.Q., Jiang, W.A.: A piezoelectric energy harvester based on internal resonance. Acta. Mech. Sin. 31, 223–228 (2015)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Sun, S., Cao, S.Q.: Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function. Acta Mech. Sin. 33, 200–207 (2017)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Karami, M.A., Inman, D.J.: Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems. J. Sound Vib. 330, 5583–5597 (2011)CrossRefGoogle Scholar
  27. 27.
    Stanton, S.C., Owens, B., Mann, B.P.: Harmonic balance analysis of the bistable piezoelectric inertial generator. J. Sound Vib. 331, 3617–3627 (2012)CrossRefGoogle Scholar
  28. 28.
    Kim, P., Seok, J.: A multi-stable energy harvester: dynamic modeling and bifurcation analysis. J. Sound Vib. 333, 5525–5547 (2014)CrossRefGoogle Scholar
  29. 29.
    Abed, I., Kacen, N., Bouhaddi, N., et al.: Multi-modal vibration energy harvesting approach based on nonlinear oscillator arrays under magnetic levitation. Smart Mater. Struct. 25, 025018 (2016)CrossRefGoogle Scholar
  30. 30.
    Daqaq, M.F., Stabler, C., Qaroush, Y., et al.: Investigation of power harvesting via parametric excitations. J. Intell. Mater. Syst. Struct. 20, 545–557 (2009)CrossRefGoogle Scholar
  31. 31.
    Jia, Y., Yan, J., Soga, K., et al.: Parametrically excited MEMS vibration energy harvesters with design approaches to overcome the initiation threshold amplitude. J. Micromech. Microeng. 23, 114007 (2013)CrossRefGoogle Scholar
  32. 32.
    Jia, Y., Seshia, A.A.: An auto-parametrically excited vibration energy harvester. Sens. Actuators A 220, 69–75 (2014)CrossRefGoogle Scholar
  33. 33.
    Jia, Y., Yan, J., Soga, K., et al.: Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude. Smart Mater. Struct. 23, 065011 (2014)CrossRefGoogle Scholar
  34. 34.
    Jia, Y., Yan, J., Soga, K., et al.: A parametrically excited vibration energy harvester. J. Intell. Mater. Syst. Struct. 25, 278–289 (2014)CrossRefGoogle Scholar
  35. 35.
    Abdelkefi, A., Nayfeh, A.H., Hajj, M.R.: Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters. Nonlinear Dyn. 67, 1147–1160 (2012)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Bitar, D., Kacem, N., Bouhaddi, N., et al.: Collective dynamics of periodic nonlinear oscillators under simultaneous parametric and external excitations. Nonlinear Dyn. 82, 749–766 (2015)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Chiba, M., Shimazaki, N., Ichinohe, K.: Dynamic stability of a slender beam under horizontal–vertical excitations. J. Sound Vib. 333, 1442–1472 (2014)CrossRefGoogle Scholar
  38. 38.
    Kacem, N., Baguet, S., Dufour, R., et al.: Stability control of nonlinear micromechanical resonators under simultaneous primary and superharmonic resonances. Appl. Phys. Lett. 98, 193507 (2011)CrossRefGoogle Scholar
  39. 39.
    Kacem, N., Baguet, S., Duraffourg, L., et al.: Overcoming limitations of nanomechanical resonators with simultaneous resonances. Appl. Phys. Lett. 107, 073105 (2015)CrossRefGoogle Scholar
  40. 40.
    Jallouli, A., Kacem, N., Bouhaddi, N.: Stabilization of solitons in coupled nonlinear pendulums with simultaneous external and parametric excitations. Commun. Nonlinear Sci. Numer. Simul. 42, 1–11 (2017)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Souayeh, S., Kacem, N.: Computational models for large amplitude nonlinear vibrations of electrostatically actuated carbon nanotube-based mass sensors. Sens. Actuators A Phys. 208, 10–20 (2014)CrossRefGoogle Scholar
  42. 42.
    Kacem, N., Baguet, S., Hentz, S., et al.: Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors. Int. J. Non-Linear Mech. 46, 532–542 (2011)CrossRefGoogle Scholar
  43. 43.
    Jallouli, A., Kacem, N., Bourbon, G., et al.: Pull-in instability tuning in imperfect nonlinear circular microplates under electrostatic actuation. Phys. Lett. A 380, 3886–3890 (2016)CrossRefGoogle Scholar
  44. 44.
    Juillard, J., Bonnoit, A., Avignon, E., et al.: From MEMS to NEMS: closed-loop actuation of resonant beams beyond the critical duffing amplitude. In: Proceedings of IEEE Sensors Conference, Lecce, Italy, 510–513 (2008).  https://doi.org/10.1109/ICSENS.2008.4716489
  45. 45.
    Kacem, N., Baguet, S., Hentz, S., et al.: Nonlinear phenomena in nanomechanical resonators: mechanical behaviors and physical limitations. Mécan. Ind. 11, 521–529 (2010)CrossRefGoogle Scholar
  46. 46.
    Kacem, N., Baguet, S., Hentz, S., et al.: Pull-in retarding in nonlinear nanoelectromechanical resonators under superharmonic excitation. J. Comput. Nonlinear Dyn. 7, 021011 (2012)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil and Hydraulic EngineeringHefei University of TechnologyHefeiChina

Personalised recommendations