Benchmark analysis of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates

  • B. K. Jha
  • M. C. RayEmail author


This paper is concerned with the derivation of exact solutions for the responses of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates. An electro-elastic finite element model is also developed based on the layer wise first order shear deformation theory for computing the responses of the bimorphs under general boundary and loading conditions. Both series and parallel connections of the piezoelectric layers of the bimorphs are considered. The responses computed by the finite element model excellently match with that obtained by the exact solutions. The induced electric potential in case of the bimorph in which the piezoelectric layers are connected in series is significantly larger than that in case of the bimorph with piezoelectric layers connected in parallel. If the thickness of the piezoelectric layers and the substrate remain same, the piezoelectric bimorph composed of antisymmetric angle-ply substrate beam is capable of inducing more electric potential than the bimorphs with cross-ply substrate beams. Also, if the bimorph is cantilever, it induces significantly more electric potential than when it is simply supported. Optimum thickness of the piezoelectric layers of the bimorph and unimorph harvesters has been determined. Most importantly, it is found that the bimorph with its piezoelectric layers connected in series performs significantly better than the unimorph if the mass and volume of the piezoelectric layers and the substrates remain same. The results presented here may serve as the benchmark results for verifying experimental and numerical models.


Energy harvester Smart materials Smart structures Exact solutions Bimorph 


  1. Amini, Y., Emdad, H., Farid, M.: Finite element modeling of functionally graded piezoelectric harvesters. Compos. Struct. 129, 165–176 (2015)CrossRefGoogle Scholar
  2. Chen, Xu-rui, Yang, Tong-qing, Wang, W., Yao, Xi: Vibration energy harvesting with a clamped piezoelectric circular diaphragm. Ceram. Int. 38S, S271–S274 (2012)CrossRefGoogle Scholar
  3. Danesh-Yazdi, A.H., Elvin, N., Andreopoulos, Y.: Green’s function method for piezoelectric energy harvesting beams. J. Sound Vib. 333, 3092–3108 (2014)CrossRefGoogle Scholar
  4. De Marqui Junior, C., Erturk, A., Inman, D.J.: An electromechanical finite element model for piezoelectric energy harvester plates. J. Sound Vib. 327, 9–25 (2009)CrossRefGoogle Scholar
  5. DuToit, N.E., Wardle, B.L.: Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA 45(5), 1126–1137 (2007)CrossRefGoogle Scholar
  6. Elvin, N., Erturk, A.: Advances in Energy Harvesting Methods. Springer, New York (2013)CrossRefGoogle Scholar
  7. Erturk, A., Inman, D.J.: Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. 17, 065016 (2008b)CrossRefGoogle Scholar
  8. Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. ASME J. Vib. Acoust. 130(4), 041002-1–041002-15 (2008a)CrossRefGoogle Scholar
  9. Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18, 025009 (2009)CrossRefGoogle Scholar
  10. Erturk, A., Renno, J.M., Inman, D.J.: Modeling of piezoelectric energy harvesting from an L-shaped beam-mass structure with an application to UAVs. J. Intell. Mater. Syst. Struct. 20, 529–544 (2008)CrossRefGoogle Scholar
  11. Guan, M.J., Liao, W.H.: On the efficiencies of piezoelectric energy harvesting circuits towards storage device voltages. Smart Mater. Struct. 16, 498 (2007)CrossRefGoogle Scholar
  12. Kundu, S., Nemade, H.B.: Modeling and simulation of a Piezoelectric vibration energy harvester. Proc. Eng. 144, 568–575 (2016)CrossRefGoogle Scholar
  13. Leadenham, S., Erturk, A.: Unified nonlinear electroelastic dynamics of a bimorph piezoelectric cantilever for energy harvesting, sensing, and actuation. Nonlinear Dyn. 79(3), 1727–1743 (2014)CrossRefGoogle Scholar
  14. Mam, K., Peigney, M., Siegert, D.: Finite strain effects in piezoelectric energy harvesters under direct and parametric excitations. J. Sound Vib. 389, 411–437 (2017)CrossRefGoogle Scholar
  15. Priya, S.: Advances in energy harvesting using low profile piezoelectric transducers. J. Electroceram. 19, 167–184 (2007)CrossRefGoogle Scholar
  16. Reddy, J.N.: Mechanics of Laminated Composite Plates, Theory, and Analysis. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  17. Rosa, M., De Marqui Junior, C.: Modeling and analysis of a piezoelectric energy harvester with varying cross section. Shock Vib. 2014, Article No. 930503 (2014)Google Scholar
  18. Roundy, S.: On the effectiveness of vibration-based energy harvesting. J. Intell. Mater. Syst. Struct. 16(10), 809–823 (2005)CrossRefGoogle Scholar
  19. Roundy, S., Leland, E.S., Baker, J., Carleton, E., Reilly, E., Lai, E., Otis, B., Rabaey, J.M., Wright, P.K., Sundararajan, V.: Improving power output for vibration-based energy scavengers. IEEE Pervasive Comput. 4(1), 28–36 (2005)CrossRefGoogle Scholar
  20. Satya, A., Bowen, C.R., Kim, H.A., Rysak, A., Litak, G.: Experimental analysis of the dynamical response of energy harvesting devices based on bistable laminated plates. Meccanica 50(8), 1961–1970 (2015)CrossRefGoogle Scholar
  21. Shu, Y.C., Lien, I.C.: Analysis of power output for piezoelectric energy harvesting systems. Smart Mater. Struct. 15, 1499–1512 (2006)CrossRefGoogle Scholar
  22. Smith, W.A., Auld, B.A.: Modeling 1–3 composite piezoelectrics: thickness mode oscillations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 31, 40–47 (1991)CrossRefGoogle Scholar
  23. Sodano, H.A., Inman, D.J.: Estimation of electric charge output for piezoelectric energy harvesting. Strain 40(2), 49–58 (2004)CrossRefGoogle Scholar
  24. 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
  25. Tan, T., Yan, Z., Hajj, M.: Electromechanical decoupled model for cantilever-beam piezoelectric energy harvesters. Appl. Phys. Lett. 109(10), 101908 (2016)CrossRefGoogle Scholar
  26. Xei, X.D., Wang, Q.: A study on a high efficient cylinder composite piezoelectric energy harvester. Compos. Struct. 161, 237–245 (2017)CrossRefGoogle Scholar
  27. Yan, Z., Hajj, M.R.: Nonlinear performance of an auto parametric vibration-based piezoelectric energy harvester. J. Intell. Mater. Syst. Struct. 28(2), 254–271 (2017)CrossRefGoogle Scholar
  28. Yang, W., Towfighian, S.: A hybrid nonlinear vibration energy system. Mech. Syst. Signal Process. 90, 317–333 (2017)CrossRefGoogle Scholar
  29. Zhang, L., Williams, K.A., Xei, Z.: evaluation of analytical and finite element modeling on coupled field dynamics of piezoelectric cantilever bimorph harvester. Appl. Mech. Mater. 284–287, 1846–1850 (2013a)CrossRefGoogle Scholar
  30. Zhang, L., Williams, K.A., Xei, Z.: Evaluation of analytical and finite element modeling on coupled field dynamics of piezoelectric cantilever bimorph harvester. Trans. Can. Soc. Mech. Eng. 37(3), 621–629 (2013b)CrossRefGoogle Scholar
  31. Zhang, L., Williams, K.A., Xei, Z.: Development and validation of an enhanced couple field model for PZT cantilever bimorph energy harvester. Math. Prob. Eng. 2013, 980161 (2013c)Google Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

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