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Size effect of tip mass on performance of cantilevered piezoelectric energy harvester with a dynamic magnifier

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Abstract

A distributed-parameter model of cantilevered piezoelectric beam with a dynamic magnifier has been proposed for the efficient analysis of a piezoelectric energy harvester, but there appears no beam model suitable for a piezoelectric energy harvester with tip mass offset and a dynamic magnifier. To deal with tip mass offset, the size effect of tip mass offset on the kinetic equation and boundary condition has been considered. A modified model of cantilevered piezoelectric energy harvester with tip mass offset and a dynamic magnifier has been developed by using the generalized Hamilton’s principle. Analytical formulation of the eigenfunction and natural frequency of the modified model have been presented. The modified model has been demonstrated by parametric studies. The results obtained show that the harvesting power can be dramatically enhanced with proper selection of the design parameters of the dynamic magnifier and tip mass offset. The tip mass offset significantly affects the accuracy of the analysis. It is observed that even a small change in tip mass geometry results in a substantial change of energy harvester performance, not only to change the resonant frequency but also to affect the strain distribution along the energy harvester length. The modified model is more suitable for the harvester with tip mass offset and dynamic magnifier.

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References

  1. Anton, S.R., Sodano, H.A.: A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct. 16, R1–R21 (2007)

    Article  Google Scholar 

  2. Kim, H., Kim, J.H., Kim, J.: A review of piezoelectric energy harvesting based on vibration. Int. J. Precis. Eng. Manuf. 12, 1129–1141 (2011)

    Article  Google Scholar 

  3. Caliò, R., Rongala, U.B., Camboni, D., Milazzo, M., Stefanini, C., de Petris, G., Oddo, C.M.: Piezoelectric energy harvesting solutions. Sensors 14(3), 4755–4790 (2014)

    Article  Google Scholar 

  4. Hagood, N.W., Chung, W.H., Von Flotow, A.: Modelling of piezoelectric actuator dynamics for active structural control. J. Intell. Mater. Syst. Struct. 1, 327–354 (1990)

    Article  Google Scholar 

  5. Schoeftner, J., Krommer, M.: Single point vibration control for a passive piezoelectric Bernoulli-Euler beam subjected to spatially varying harmonic loads. Acta Mech. 223, 1983–1998 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Krommer, M.: On the correction of the Bernoulli-Euler beam theory for smart piezoelectric beams. Smart Mater. Struct. 10, 668–680 (2001)

    Article  Google Scholar 

  8. Roundy, S., Wright, P.K.: A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct. 13, 1131–1142 (2004)

    Article  Google Scholar 

  9. Sodano, H.A., Park, G., Inman, D.J.: Estimation of electric charge output for piezoelectric energy harvesting. Strain 40, 49–58 (2004)

    Article  Google Scholar 

  10. DuToit, N.E., Wardle, B.L., Kim, S.: Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. Integr. Ferroelectr. 71, 121–160 (2005)

    Article  Google Scholar 

  11. DuToit, N.E., Wardle, B.L.: Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA J. 45, 1126–1137 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Erturk, A., Inman, D.J.: On mechanical modeling of cantilevered piezoelectric vibration energy harvesters. J. Intell. Mater. Syst. Struct. 19, 1311–1325 (2008)

    Article  Google Scholar 

  14. Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18, 025009 (2009)

    Article  Google Scholar 

  15. Stephen, N.G.: On energy harvesting from ambient vibration. J. Sound Vib. 293, 409–425 (2006)

    Article  Google Scholar 

  16. Renno, J.M., Daqaq, M.F., Inman, D.J.: On the optimal energy harvesting from a vibration source. J. Sound Vib. 320, 386–405 (2009)

    Article  Google Scholar 

  17. De Marqui Jr., C., Erturk, A., Inman, D.J.: An electromechanical finite element model for piezoelectric energy harvester plates. J. Sound Vib. 327, 9–25 (2009)

    Article  Google Scholar 

  18. Lumentut, M.F., Howard, I.M.: Intrinsic electromechanical dynamic equations for piezoelectric power harvesters. Acta Mech. 228, 631–650 (2017)

    Article  MathSciNet  Google Scholar 

  19. Lumentut, M.F., Howard, I.M.: Electromechanical analysis of an adaptive piezoelectric energy harvester controlled by two segmented electrodes with shunt circuit networks. Acta Mech. 228, 1321–1341 (2017)

    Article  MATH  Google Scholar 

  20. DuToit, N.E., Wardle, B.L., Kim, S.: Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. Integr. Ferroelectr. 71, 121–160 (2005)

    Article  Google Scholar 

  21. Kim, M., Hoegen, M., Dugundji, J., Wardle, B.L.: Modeling and experimental verification of proof mass effects on vibration energy harvester performance. Smart Mater. Struct. 19, 045023 (2010)

    Article  Google Scholar 

  22. Kim, E.J., Kim, Y.Y.: Analysis of piezoelectric energy harvesters of a moderate aspect ratio with a distributed tip mass. ASME J. Vib. Acoust. 133, 041010 (2011)

    Article  Google Scholar 

  23. Wang, H., Meng, Q.: Analytical modeling and experimental verification of vibration-based piezoelectric bimorph beam with a tip-mass for power harvesting. Mech. Syst. Signal Process. 36, 193–209 (2013)

    Article  Google Scholar 

  24. Lumentut, M.F., Howard, I.M.: Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations. Smart Mater. Struct. 23, 095037 (2014)

    Article  Google Scholar 

  25. Lumentut, M.F., Howard, I.M.: Parametric design-based modal damped vibrational piezoelectric energy harvesters with arbitrary proof mass offset: Numerical and analytical validations. Mech. Syst. Signal Process. 68–69, 562–586 (2016)

    Article  Google Scholar 

  26. Shindo, Y., Narita, F.: Dynamic bending/torsion and output power of S-shaped piezoelectric energy harvesters. Int. J. Mech. Mater. Des. 10, 305–311 (2014)

    Article  Google Scholar 

  27. Zhou, W., Penamalli, G.R., Zuo, L.: An efficient vibration energy harvester with a multi-mode dynamic magnifier. Smart Mater. Struct. 21, 015014 (2012)

    Article  Google Scholar 

  28. Aldraihem, O., Baz, A.: Energy harvester with a dynamic magnifier. J. Intell. Mater. Syst. Struct. 22, 521–530 (2011)

    Article  Google Scholar 

  29. Aladwani, A., Arafa, M., Aldraihem, O., Baz, A.: Cantilevered piezoelectric energy harvester with a dynamic magnifier. ASME J. Vib. Acoust. 34, 031004 (2012)

    Article  Google Scholar 

  30. Aladwani, A., Aldraihem, O., Baz, A.: A distributed parameter cantilevered piezoelectric energy harvester with a dynamic magnifier. Mech. Adv. Mater. Struct. 21, 566–578 (2014)

    Article  Google Scholar 

  31. Rajagopal, K.R.: A note on a reappraisal and generalization of the Kelvin-Voigt model. Mech. Res. Commun. 36, 232–235 (2009)

    Article  MATH  Google Scholar 

  32. Banks, H.T., Inman, D.J.: On damping mechanisms in beams. ASME J. Appl. Mech. 58, 716–723 (1991)

    Article  MATH  Google Scholar 

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Correspondence to Jianguo Wang.

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Tang, L., Wang, J. Size effect of tip mass on performance of cantilevered piezoelectric energy harvester with a dynamic magnifier. Acta Mech 228, 3997–4015 (2017). https://doi.org/10.1007/s00707-017-1910-8

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  • DOI: https://doi.org/10.1007/s00707-017-1910-8

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