Piezoelectric Energy Harvesting from a Bridge Subjected to Time-Dependent Moving Loads Using Finite Elements

  • Kouider BendineEmail author
  • Mohamed Hamdaoui
  • Benallel Farouk Boukhoulda
Research Article - Mechanical Engineering


The present paper addresses vibration energy harvesting from a bridge subjected to time-dependent moving loads thanks to a cantilever piezoelectric harvester fixed beneath the bridge. A finite element model of the bridge based on Kirchhoff plate assumptions, Hamilton principle and Newmark integration scheme, for time domain analysis, is considered. The time-varying acceleration of the bridge, submitted to a moving load, is then applied as a base excitation to an electromechanical model of the harvester. Different types of moving loads are considered (constant, harmonic, broadband and narrow-band). In the case of constant or harmonic moving loads, the obtained results confirm previous findings in the literature: for a moving load frequency equal to the natural frequency of the bridge, the harvested energy is maximal when the harvester is located at the maximum amplitude of the bridge’s corresponding mode shape. These results are not confirmed in the case of realistic moving loads with broadband or narrow-banded frequency spectrum pointing out the weakness of the harmonic analysis and the dependence of the harvested energy on the frequency spectrum of the moving load which appears to be with the moving load velocity the two key parameters for energy harvesting.


Piezoelectric energy harvesting Finite element Moving load 


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  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, 43001 (2008)CrossRefGoogle Scholar
  2. 2.
    Erturk, A.; Inman, D.J.: Piezoelectric Energy Harvesting. Wiley, New York (2011)CrossRefGoogle Scholar
  3. 3.
    Anton, S.R.; Sodano, H.A.: A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct. 16, R1 (2007)CrossRefGoogle Scholar
  4. 4.
    Abdelkefi, A.: Aeroelastic energy harvesting: a review. Int. J. Eng. Sci. 100, 112–135 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ansari, M.H.; Karami, M.A.: Experimental investigation of fan-folded piezoelectric energy harvesters for powering pacemakers. Smart Mater. Struct. 26, 65001 (2017)CrossRefGoogle Scholar
  6. 6.
    Upadrashta, D.; Yang, Y.: Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction. Smart Mater. Struct. 24, 45042 (2015)CrossRefGoogle Scholar
  7. 7.
    Brissaud, M.: Matériaux Piézoélectriques: Caractérisation. Modélisation et Vibration. PPUR presses polytechniques, Lausanne (2007)zbMATHGoogle Scholar
  8. 8.
    Crawley, E.F.; De Luis, J.: Use of piezoelectric actuators as elements of intelligent structures. AIAA J. 25, 1373–1385 (1987)CrossRefGoogle Scholar
  9. 9.
    Yang, J.: An Introduction to the Theory of Piezoelectricity, vol. 9. Springer, Berlin (2004)Google Scholar
  10. 10.
    Aladwani, A.; Aldraihem, O.; Baz, A.: Single degree of freedom shear-mode piezoelectric energy harvester. J. Vib. Acoust. 135, 51011 (2013)CrossRefGoogle Scholar
  11. 11.
    Stephen, N.G.: On energy harvesting from ambient vibration. J. Sound Vib. 293, 409–425 (2006)CrossRefGoogle Scholar
  12. 12.
    Tang, L.; Yang, Y.: A multiple-degree-of-freedom piezoelectric energy harvesting model. J. Intell. Mater. Syst. Struct. 23, 1631–1647 (2012)CrossRefGoogle Scholar
  13. 13.
    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 (2009)CrossRefGoogle Scholar
  14. 14.
    Erturk, A.; Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vib. Acoust. 130, 41002 (2008)CrossRefGoogle Scholar
  15. 15.
    Junior, C.D.M.; Erturk, A.; Inman, D.J.: An electromechanical finite element model for piezoelectric energy harvester plates. J. Sound Vib. 327, 9–25 (2009)CrossRefGoogle Scholar
  16. 16.
    Lin, Z.-Q.; Gea, H.C.; Liu, S.-T.: Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization. Acta Mech. Sin. 27, 730 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Erturk, A.; Inman, D.J.: Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. 17, 65016 (2008)CrossRefGoogle Scholar
  18. 18.
    Cottone, F.; Vocca, H.; Gammaitoni, L.: Nonlinear energy harvesting. Phys. Rev. Lett. 102, 80601 (2009)CrossRefGoogle Scholar
  19. 19.
    Mann, B.P.; Sims, N.D.: Energy harvesting from the nonlinear oscillations of magnetic levitation. J. Sound Vib. 319, 515–530 (2009)CrossRefGoogle Scholar
  20. 20.
    Stanton, S.C.; McGehee, C.C.; Mann, B.P.: Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator. Phys. Nonlinear Phenom. 239, 640–653 (2010)CrossRefzbMATHGoogle Scholar
  21. 21.
    Adhikari, S.; Friswell, M.I.; Inman, D.J.: Piezoelectric energy harvesting from broadband random vibrations. Smart Mater. Struct. 18, 115005 (2009)CrossRefGoogle Scholar
  22. 22.
    Daqaq, M.F.: Response of uni-modal duffing-type harvesters to random forced excitations. J. Sound Vib. 329, 3621–3631 (2010)CrossRefGoogle Scholar
  23. 23.
    Litak, G.; Friswell, M.I.; Adhikari, S.: Magnetopiezoelastic energy harvesting driven by random excitations. Appl. Phys. Lett. 96, 214103 (2010)CrossRefGoogle Scholar
  24. 24.
    Halvorsen, E.: Energy harvesters driven by broadband random vibrations. J. Microelectromechanical Syst. 17, 1061–1071 (2008)CrossRefGoogle Scholar
  25. 25.
    Elvin, N.; Elvin, A.; Choi, D.H.: A self-powered damage detection sensor. J. Strain Anal. Eng. Des. 38, 115–124 (2003)CrossRefGoogle Scholar
  26. 26.
    Elvin, N.G.; Lajnef, N.; Elvin, A.A.: Feasibility of structural monitoring with vibration powered sensors. Smart Mater. Struct. 15, 977 (2006)CrossRefGoogle Scholar
  27. 27.
    Zhang, Z.; Xiang, H.; Shi, Z.: Modeling on piezoelectric energy harvesting from pavements under traffic loads. J. Intell. Mater. Syst. Struct. 27, 567–578 (2016)CrossRefGoogle Scholar
  28. 28.
    Kim, S.-H.; Ahn, J.-H.; Chung, H.-M.; Kang, H.-W.: Analysis of piezoelectric effects on various loading conditions for energy harvesting in a bridge system. Sens. Actuators Phys. 167, 468–483 (2011)CrossRefGoogle Scholar
  29. 29.
    Cahill, P.; Nuallain, N.A.N.; Jackson, N.; Mathewson, A.; Karoumi, R.; Pakrashi, V.: Energy harvesting from train-induced response in bridges. J. Bridge Eng. 19, 4014034 (2014)CrossRefGoogle Scholar
  30. 30.
    Zhang, Z.; Xiang, H.; Shi, Z.: Mechanism exploration of piezoelectric energy harvesting from vibration in beams subjected to moving harmonic loads. Compos. Struct. 179, 368–376 (2017)CrossRefGoogle Scholar
  31. 31.
    Erturk, A.: Piezoelectric energy harvesting for civil infrastructure system applications: moving loads and surface strain fluctuations. J. Intell. Mater. Syst. Struct. 22, 1959–1973 (2011)CrossRefGoogle Scholar
  32. 32.
    Ouyang, H.: Moving-load dynamic problems: a tutorial (with a brief overview). Mech. Syst. Signal Process. 25, 2039–2060 (2011)CrossRefGoogle Scholar
  33. 33.
    Frỳba, L.: Vibration of Solids and Structures under Moving Loads, vol. 1. Springer, Berlin (2013)zbMATHGoogle Scholar
  34. 34.
    Yang, Y.-B.; Yau, J.D.; Yao, Z.; Wu, Y.S.: Vehicle-Bridge Interaction Dynamics: With Applications to High-Speed Railways. World Scientific, Singapore (2004)CrossRefGoogle Scholar
  35. 35.
    De Abreu, G.; Ribeiro, J.F.; Steffen Jr., V.: Finite element modeling of a plate with localized piezoelectric sensors and actuators. J. Braz. Soc. Mech. Sci. Eng. 26, 117–128 (2004)CrossRefGoogle Scholar
  36. 36.
    Lam, K.Y.; Peng, X.Q.; Liu, G.R.; Reddy, J.N.: A finite-element model for piezoelectric composite laminates. Smart Mater. Struct. 6, 583 (1997)CrossRefGoogle Scholar
  37. 37.
    Tzou, H.S.; Tseng, C.I.: Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. J. Sound Vib. 138, 17–34 (1990)CrossRefGoogle Scholar
  38. 38.
    Chhabra, D.; Bhushan, G.; Chandna, P.: Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm. Mech. Adv. Mater. Struct. 23, 272–280 (2016)CrossRefGoogle Scholar
  39. 39.
    Bathe, K.J.: Finite Element Procedures. Klaus-Jurgen Bathe, Berlin (2006)zbMATHGoogle Scholar
  40. 40.
    Bendine, K.; Boukhoulda, F.B.; Haddag, B.; Nouari, M.: Active vibration control of composite plate with optimal placement of piezoelectric patches. Mech. Adv. Mater. Struct. 26, 1455 (2017)Google Scholar
  41. 41.
    Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)CrossRefzbMATHGoogle Scholar
  42. 42.
    Narayanan, S.; Balamurugan, V.: Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. J. Sound Vib. 262, 529–562 (2003)CrossRefGoogle Scholar

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© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  • Kouider Bendine
    • 1
    Email author
  • Mohamed Hamdaoui
    • 2
  • Benallel Farouk Boukhoulda
    • 1
  1. 1.Structures and Solid Mechanical Laboratory, Mechanical DepartmentDjillali Liabès University of Sidi Bel-AbbèsCité Ben M’hidi, Sidi Bel-AbbèsAlgeria
  2. 2.CNRS, Arts et Métiers ParisTech, LEM3Université de LorraineMetzFrance

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