Journal of Marine Science and Application

, Volume 16, Issue 4, pp 465–472 | Cite as

A numerical study on piezoelectric energy harvesting by combining transverse galloping and parametric instability phenomena

  • Guilherme Rosa Franzini
  • Rebeca Caramêz Saraiva Santos
  • Celso Pupo Pesce


This paper aims to numerically investigate the effects of parametric instability on piezoelectric energy harvesting from the transverse galloping of a square prism. A two degrees-of-freedom reduced-order model for this problem is proposed and numerically integrated. A usual quasi-steady galloping model is applied, where the transverse force coefficient is adopted as a cubic polynomial function with respect to the angle of attack. Time-histories of nondimensional prism displacement, electric voltage and power dissipated at both the dashpot and the electrical resistance are obtained as functions of the reduced velocity. Both, oscillation amplitude and electric voltage, increased with the reduced velocity for all parametric excitation conditions tested. For low values of reduced velocity, 2:1 parametric excitation enhances the electric voltage. On the other hand, for higher reduced velocities, a 1:1 parametric excitation (i.e., the same as the natural frequency) enhances both oscillation amplitude and electric voltage. It has been also found that, depending on the parametric excitation frequency, the harvested electrical power can be amplified in 70% when compared to the case under no parametric excitation.


transverse galloping energy harvesting piezoelectricity parametric instability numerical simulations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The first and the thrid authors acknowledge National Research Council – CNPq for grants 310595/2015-0 and 08990/2014-5. The second author acknowledges undergraduate scholarship provided by University of São Paulo research nucleous NAP-OS (Nucleous for Research Support – Sustainable Ocean).


  1. Barrero-Gil A, Alonso G, Sanz-Andres A, 2010. Energy harvesting from transverse galloping. Journal of Sound and Vibration, 329, 2873–2883. DOI: Scholar
  2. Bernitsas MM, Raghavan K, Ben-Simos Y, Garcia EMH, 2006a. VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A new concept in generation of clean and renewable energy from fluid flow. Proceedings of OMAE2006 - International Conference on Offshore Mechanics and Artic Engineering, Hamburg. DOI: 10.1115/OMAE2006-92645Google Scholar
  3. Bernitsas MM, Ben-Simos Y, Raghavan K, Garcia EMH, 2006b. The VIVACE converter: model tests at high damping and Reynolds number around 105. Proceedings of OMAE2006 -International Conference on Offshore Mechanics and Artic Engineering, Hamburg.Google Scholar
  4. Bibo A, Daqaq MF, 2013. Energy harvesting under combined aerodynamic and base excitations. Journal of Sound and Vibration, 332, 5086–5102. DOI: Scholar
  5. Blevins R, 2001. Flow-induced vibration. Krieger.Google Scholar
  6. Doaré O, Michelin S, 2011. Piezoelectric coupling in energy harvesting fluttering flexible plates: linear stability analysis and conversion efficiency. Journal of Fluids and Structures, 27, 1357–1375. DOI: Scholar
  7. Faltinsen OM, 1993. Sea loads on ships and offshore structures. Dover publications.Google Scholar
  8. Fernandes AC, Armandei M, 2014. Low-head hydropower extraction based on torsional galloping. Renewable energy, 69, 447–452. DOI: Scholar
  9. Franzini GR, Mazzilli CEN, 2016. Nonlinear reduced-order model for parametric excitation of vertical and immersed slender rod. International Journal of Non-linear Mechanics, 80, 29–39. DOI: Scholar
  10. Franzini GR, Pesce CP, Salles R, Gonçalves RT, Fujarra ALC, Mendes P, 2015. Experimental investigation with a vertical and flexible cylinder in water: response to top motion excitation and parametric resonance. Journal of Vibration and Acoustics, 137(3), 031010–1–031010–12. DOI: Scholar
  11. Franzini GR, Pesce CP, Gonçalves RT, Mendes P, 2016a. Experimental investigations on Vortex-Induced Vibrations with a long flexible cylinder. Part II: effect of axial motion excitation in a vertical configuration. Proceedings of the 11th International Conference on Flow-Induced Vibration–FIV2016, the Hague, the Netherlands.Google Scholar
  12. Franzini GR, Santos RCS, Pesce CP, 2016b. Energy harvesting from transverse galloping enhanced by parametric excitation. Proceedings of the 11th International Conference on Flow-Induced Vibration–FIV2016, the Hague, the Netherlands.Google Scholar
  13. Grouthier C, Michelin S, Bourguet R, Modarres-Sadeghi Y, De Langre E, 2014. On the efficiency of energy harvesting using vortex-induced vibrations of cables. Journal of Fluids and Structures, 49, 427–440. DOI: Scholar
  14. Grouthier C, Michelin S, De Langre E, 2012. Optimal energy harvesting by vortex-induced vibrations in cables. Proceedings of the 10th FIV 2012 - International Conference on Flow-Induced Vibrations Conference (& Flow-Induced Noise), Dublin.Google Scholar
  15. Hoerner SF, 1965. Fluid-dynamic drag. Hoerner Fluid Dynamics.Google Scholar
  16. Korotkin AI, 2009. Added masses of ship structures. Springer. Mehmood A, Abdelkefi A, Hajj AA, Nayfeh AH, Akthar I, Nuhait, AO, 2013. Piezoelectric energy harvesting from vortex-induced vibrations of circular cylinder. Journal of Sound and Vibration, 332, 4656–4667.Google Scholar
  17. Meirovitch L, 2003. Methods of analytical dynamics. Dover Publications.Google Scholar
  18. Nayfeh AH, Mook DT, 1979. Nonlinear oscillations. John Wiley & Sons.Google Scholar
  19. Païdoussis MP, Price SJ, De Langre E, 2011. Fluid-structure interactions -cross-flow induced instabilities. Cambridge University Press.MATHGoogle Scholar
  20. Patel MH, Park HI, 1991. Dynamics of tension leg platform tethers at low tension. Part I–Mathieu instability at large parameters. Marine Structures, 4, 257–273.Google Scholar
  21. Simos AN, Pesce CP, 1997. Mathieu stability in the dynamics of TLP’s tethers considering variable tension along the length. Transactions on the Built Environment, 29, 175–186.Google Scholar
  22. Tang L, Païdoussis MP, Jiang J, 2009. Cantilever flexible plates in axial flow: Energy transfer and the concept of flutter-mill. Journal of Sound and Vibration, 326, 263–276. DOI: DOI: Scholar
  23. Xia Y, Michelin S, 2015. Fluid-solid-electric lock-in of energy harvesting piezoelectric flags. Physical Review Applied, 3(014009), 014009–1–014009–8. DOI: Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Guilherme Rosa Franzini
    • 1
  • Rebeca Caramêz Saraiva Santos
    • 1
  • Celso Pupo Pesce
    • 1
  1. 1.Escola PolitécnicaUniversity of São PauloSão PauloBrazil

Personalised recommendations