Skip to main content

Advertisement

SpringerLink
Log in

Investigations on the stability and effectiveness of wing-based piezoaeroelastic systems with combined nonlinearities

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

An investigation on the effects of the existence of freeplay, polynomial stiffness and aerodynamic nonlinearities on the dynamical responses of flutter-based piezoaeroelastic energy harvesting systems is performed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived including structural and aerodynamic nonlinearities, namely stall effects. The aerodynamic loading used in this study is the unsteady representation, based on the Duhamel formulation. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay combined with structural hardening nonlinearities before and after the linear onset of flutter. Such nonlinearities must be considered in the modeling and design of piezoaeroelastic energy harvesters, the combination of it can result in the presence of several secondary bifurcations and multiple solution regions and, therefore, affect the overall efficiency of the system. It is shown that the existence of freeplay nonlinearity leads to the possibility of harvesting energy at lower speeds than the linear onset speed of instability. As the gap size of the freeplay nonlinearity increases, the polynomial quadratic term in structural nonlinearity minimally affects the performance of the energy harvester. Further, it is shown that the stall effect should be considered when the angle of attack is higher than 2\(^{\circ }\) which significantly affect the higher Hopf bifurcations in the pitch degree of freedom.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. A. Erturk, Electromechanical modeling of piezoelectric energy harvesters. Ph.D. thesis, Virginia Polytechnic Institute and State University (2009)

  2. A. Erturk, D.J. Inman, A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vib. Acoust. 130, 25 (2008)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. A. Adhikari, M.I. Friswell, D.J. Inman, Piezoelectric energy harvesting from broadband random vibrations. Smart Mater. Struct. 18, 20 (2009)

    Article  Google Scholar 

  5. M.N. Fakhzan, A.G.A. Muthalif, Harvesting vibration energy using piezoelectric material: modeling, simulation and experimental verifications. Mechatronics 23, 61–66 (2013)

    Article  Google Scholar 

  6. S. Priya, H.C. Song, Y. Zhou, R. Varghese et al., A review on piezoelectric energy harvesting: materials, methods, and circuits. Energy Harvest. Syst. 20, 3–39 (2017)

    Article  Google Scholar 

  7. H. Elahi, M. Eugeni, P. Gaudenzi, A review on mechanisms for piezoelectric-based energy harvesters. Energies 11, 20 (2018)

    Article  Google Scholar 

  8. H. Li, D. Liu, J. Wang, X. Shang, M.R. Hajj, Broadband bimorph piezoelectric energy harvesting by exploiting bending torsion of L-shaped structure. Energy Convers. Manage. 206, 25 (2020)

    Google Scholar 

  9. N. Tran, M.H. Ghayesh, M. Arjomandi, Ambient vibration energy harvesters: a review on nonlinear techniques for performance enhancement. Int. J. Eng. Sci. 127, 162–185 (2018)

    Article  MathSciNet  Google Scholar 

  10. B.H.K. Lee, S. Price, Y. Wong, Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos. Prog. Aerosp. Sci. 35, 205–334 (1999)

    Article  Google Scholar 

  11. C. De Marqui Jr., F.D. Marques, Nonlinear behavior of a typical airfoil section with control surface nonlinearities. In: Proceedings of the 6th Brazilian Conference on Dynamics, Control and Their Applications —DINCON 2007, São José do Rio Preto, Brazil (2007)

  12. A. Erturk, W.G.R. Vieira, C. De Marqui, Inman D.J. Jr., On the energy harvesting potential of piezoaeroelastic systems. Appl. Phys. Lett. 96, 184103 (2010)

    Article  ADS  Google Scholar 

  13. V.C. Sousa, M. Anicezio, C. De Marqui, A. Erturk, Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment. Smart Mater. Struct. 20, 094007 (2011)

    Article  ADS  Google Scholar 

  14. A. Abdelkefi, R. Vasconcellos, A.H. Nayfeh, M.R. Hajj, An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system. Nonlinear Dyn. 71, 159–173 (2012)

    Article  MathSciNet  Google Scholar 

  15. A. Abdelkefi, A.H. Nayfeh, M.R. Hajj, Modeling and analysis of piezoaeroelastic energy harvesters. Nonlinear Dyn. 67, 925–939 (2012)

    Article  MathSciNet  Google Scholar 

  16. H. Djojodihardjo, Aeroelastic and performance baseline analysis of piezoaeroelastic wing section for energy harvester. In: First International Symposium on Flutter and its Application (2016)

  17. C. De Marqui Jr., D. Tan, A. Erturk, On the electrode segmentation for piezoelectric energy harvesting from nonlinear limit cycle oscillations in axial flow. J. Fluids Struct. 82, 492–504 (2018)

    Article  Google Scholar 

  18. C. Bao, Y. Dai, P. Wang, G. Tang, A piezoelectric energy harvesting scheme based on stall flutter of airfoil section. Eur. J. Mech. B Fluids 20, 20 (2019)

    MathSciNet  Google Scholar 

  19. J.A.C. Dias, V.C. Sousa, A. Erturk, C. De Marqui, Jr., Nonlinear piezoelectric plate framework for aeroelastic energy harvesting and actuation applications. Smart Mater. Struct. 29, 20 (2020)

  20. M. di Bernard, C.J. Budd, A.R. Champneys, P. Kowalczyk, Piecewise-Smooth Dynamical Systems (Springer, Berlin, 2008)

    MATH  Google Scholar 

  21. A. Abdelkefi, R. Vasconcellos, F.D. Marques, M.R. Hajj, Modeling and identification of freeplay nonlinearity. J. Sound Vib. 331, 1898–1907 (2012)

    Article  ADS  Google Scholar 

  22. R. Vasconcellos, A. Abdelkefi, M.R. Hajj, F.D. Marques, Grazing bifurcation in aeroelastic systems with freeplay nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 20, 20 (2013)

    MATH  Google Scholar 

  23. R. Vasconcellos, A. Abdelkefi, Phenomena and characterization of grazing-sliding bifurcations in aeroelastic systems with discontinuous impact effects. J. Sound Vib. 358, 315–323 (2015)

  24. A. Bouma, E. Le, R. Vasconcellos, A. Abdelkefi, Effective design and characterization of flutter-based piezoelectric energy harvesters with discontinuous nonlinearities. Energy 238, 25 (2022)

    Article  Google Scholar 

  25. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep. 496, 413–433 (1934)

  26. M. Ghommem, A.H. Nayfeh, M.R. Hajj, Control of limit cycle oscillations of a two-dimensional aeroelastic system. Math. Probl. Eng. 20, 20 (2010)

    MATH  Google Scholar 

  27. P.S. Beran, T.W. Strganac, K. Kim, C. Nichkawde, Studies of store-induced limit-cycle oscillations using a model with full system nonlinearities. Nonlinear Dyn. 37, 323–339 (2004)

    Article  Google Scholar 

  28. W. Yossri, A. Bouma, S. Ben Ayed, R. Vasconcellos, A. Abdelkefi, Insights on the unsteadiness and stall effects on the characteristics and responses of continuous wing-based systems. Nonlinear Dyn. 20, 20 (2021)

  29. A.O. Nuhait, D.T. Mook, Aeroelastic behavior of flat plates moving near the ground. J. Aircr. 47, 25 (2010)

    Article  Google Scholar 

  30. A. Abdelkefi, A.H. Nayfeh, M.R. Hajj, Enhancement of power harvesting from piezoaeroelastic system. Nonlinear Dyn. 68, 531–541 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, 88003, USA

    Adam Bouma & Abdessattar Abdelkefi

  2. São Paulo State University (UNESP), São João da Boa Vista, Brazil

    Rui Vasconcellos

Authors
  1. Adam Bouma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui Vasconcellos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdessattar Abdelkefi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdessattar Abdelkefi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bouma, A., Vasconcellos, R. & Abdelkefi, A. Investigations on the stability and effectiveness of wing-based piezoaeroelastic systems with combined nonlinearities. Eur. Phys. J. Spec. Top. 231, 1537–1556 (2022). https://doi.org/10.1140/epjs/s11734-022-00491-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00491-z

Search

Navigation