Abstract
The dynamic behaviour of an aeroelastic energy harvester using a piezoelectric transducer is studied. An important question in applications of energy harvesting is how to increase the efficiency of energy conversion. The study of both mechanical and electrical nonlinear terms has proven important in this context, both to provide more accurate models and to aid the design of purposely nonlinear systems. Here, the influence of plunge cubic nonlinear stiffness and nonlinear piezoelectrical coupling is investigated with respect to flutter speed, mechanical and electrical power. Different combinations of nonlinear terms are explored and compared to the linear case. The influence of the nonlinear coefficients and of the parameters of the electrical domain on the behaviour of the system are analysed analytically via the method of multiple scales (MMS) and numerically via a fourth-order Runge–Kutta method (RK). A Poincaré section method is proposed to determine the period of oscillations of the nonlinear systems at flutter. The results indicate that nonlinear stiffness has more influence in increasing flutter speed, and nonlinear piezoelectrical coupling has more influence in increasing electrical power. More energy is transferred from the pitch motion than from the plunge motion. Flutter speed, mechanical and electrical power increase with nonlinear stiffness, indicating that neglecting this characteristic can lead to underestimation of flutter speed and harvested energy.
Similar content being viewed by others
References
Sodano HA, Inman DJ, Park G (2004) A review of power harvesting from vibration using piezoelectric materials. Shock Vib Dig 36:197–205
Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 16:1–21
Harb A (2011) Energy harvesting: State-of-the-art. Renew Energy 36:2641–2654
Safaei M, Sodano HA, Anton SR (2019) A review of energy harvesting using piezoelectric materials: state-of-the-art a decade later (2008–2018). Smart Mater Struct 28(11):113001
Amirtharajah R, Chandrakasan AP (1998) Self-powered signal processing using vibration-based power generation. IEEE J Solid-State Circuits 33:687–695
Roundy S, Wright P.K (2004) A piezoelectric vibration based generator for wireless electronics. Smart Mater Struct. 13
Gatti G, Brennan MJ, Tehrani MG, Thompson DJ (2016) Harvesting energy from the vibration of a passing train using a single-degree-of-freedom oscillator. Mech Syst Signal Process 66–67:785–792
Yang G, Stark BH, Hollis SJ, Burrow SG (2014) Challenges for energy harvesting systems under intermittent excitation. IEEE J Emerg and Sel Topics Circuits Syst 4(3):364–374
Brennan M.J, Gatti G (2017) Harvesting energy from time-limited harmonic vibrations: mechanical considerations. J Vib Acoust. 139(5)
Tang L, Paidoussis M, Jiang J (2009) Cantilevered flexible plates in axial flow: energy transfer and the concept of flutter-mill. J Sound Vib 326:263–276
Akaydin HD, Elvin N, Y, A, (2010) Wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials. Exp Fluids 49:291–304
Erturk A, Vieira WGR, Marqui C Jr (2010) On the energy harvesting potential of piezoaeroelastic systems. Appl Phys Lett 96:184103
Bibo A, Daqaq MF (2013) Energy harvesting under combined aerodynamic and base excitations. J Sound Vib 332(20):5086–5102
Jonsson E, Riso C, Lupp C.A, Cesnik C.E.S, Martins J, Epureanu B.I (2019) Flutter and post-flutter constraints in aircraft design optimization. Prog Aerosp Sci
Lu Z, Chen J, Ding H, Chen L (2022) Energy harvesting of a fluid-conveying piezoelectric pipe. Appl Math Model 107:165–181
Zhang Y, Guo K, Wang D, Chen C, Li X (2017) Energy conversion mechanism and regenerative potential of vehicle suspensions. Energy 119:961–970
Zuo L, Scully B, Shestani J, Zhou Y (2010) Design and characterization of an electromagnetic energy harvester for vehicle suspensions. Smart Mater Struct 19:045003
Kuhnert WM, Cammarano A, Silveira M, Gonçalves P (2021) Optimum design of electromechanical vibration isolators. J Vib Cont 27:169–184
Hu Y, Wang X, Qin Y, Li Z, Wang C, Wu H (2022) A robust hybrid generator for harvesting vehicle suspension vibration energy from random road excitation. Appl Energy 309:118506
Sugino C, Erturk A (2018) Analysis of multifunctional piezoelectric metastructures for low-frequency bandgap formation and energy harvesting. J Phys D: Appl Phys 51(21):215103
Bukhari M, Barry O (2020) Simultaneous energy harvesting and vibration control in a nonlinear metastructure: A spectro-spatial analysis. J Sound Vib 473:115215
Vasconcellos D.P, Cruz R.S, Fernandes J.C.M, Silveira M (2022) Vibration attenuation and energy harvesting in metastructures with nonlinear absorbers conserving mass and strain energy. Eur Phys J Special Topics, 1–9
Wen Z, Wang W, Khelif A, Djafari-Rouhani B, Jin Y (2022) A perspective on elastic metastructures for energy harvesting. Appl Phys Lett 120(2):020501
Stephen NG (2006) On energy harvesting from ambient vibration. J Sound Vib 293(1–2):409–425
Yang Z, Erturk A, Zu J (2017) On the efficiency of piezoelectric energy harvesters. Extreme Mech Lett 15:26–37
Marqui C Jr, Erturk A (2013) Electroaeroelastic analysis of airfoil-based wind energy harvesting using piezoelectric transduction and electromagnetic induction. J Intell Mater Syst Struct 24:846–854
Tsushima N, Su W (2017) Flutter suppression for highly flexible wings using passive and active piezoelectric effects. Aerosp Sci Technol 65:78–89
Jung HJ, Lee SW (2011) The experimental validation of a new energy harvesting system based on the wake galloping phenomenon. Smart Mater Struct 20:055022
Abdelkefi A, Hajj MR, Nayfeh AH (2013) Piezoelectric energy harvesting from transverse galloping of bluff bodies. Smart Mater Struct 22(1):015014
Zhang LB, Abdelkefi A, Dai HL, Naseer R, Wanga L (2017) Design and experimental analysis of broadband energy harvesting from vortex-induced vibrations. J Sound Vib 408:210–219
Daqaq MF, Masana R, Erturk A, Quinn DD (2014) On the role of nonlinearities in vibratory energy harvesting: A critical review and discussion. Appl Mech Rev 66:040801
Cottone F, Vocca H, Gammaitoni L (2009) Nonlinear energy harvesting. Phys Rev Lett 102:080601
Erturk A, Hoffmann J, Inman DJ (2009) A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl Phys Lett 94:254102
Tehrani MG, Elliott SJ (2014) Extending the dynamic range of an energy harvester using nonlinear damping. J Sound Vib 333:623–629
Price SJ, Lee BHK, Alighanbari H (1994) Postinstability behavior of a two-dimensional airfoil with a structural nonlinearity. J Aircraft 31:395–401
Tang D, Dowell EH (2006) Flutter and limit-cycle oscillations for a wing-store model with freeplay. J Aircraft 43:487–503
Sousa VC, Anicézio MM, Marqui C Jr, Erturk A (2011) Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment. Smart Mater Struct 20:094007
Abdelkefi A, Nayfeh AH, Hajj MR (2012) Modeling and analysis of piezoaeroelastic energy harvesters. Nonlinear Dynam 67(2):925–939
Crawley EF, Anderson EH (1990) Detailed models of piezoceramic actuation of beams. J Intell Mater Syst Struct 1:4–25
Toit NE, Wardle BL (2007) Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA J 45:1126–1137
Triplett A, Quinn DD (2009) The effect of non-linear piezoelectric coupling on vibration-based energy harvesting. J Intell Mater Syst Suct 20(16):1959–1967
Balthazar J.M, Rocha R.D, Brasil R.L.M.F, Tusset A.M, Pontes Jr B.R, Silveira M (2014) Mode saturation, mode coupling and energy harvesting from ambient vibration in a portal frame structure. In: ASME 2014 International design engineering technical conferences
Abdelkefi A, Nayfeh AH, Hajj MR (2012) Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation. Nonlinear Dyn 67:1221–1232
Leadenham S, Erturk A (2015) Unified nonlinear electroelastic dynamics of a bimorph piezoelectric cantilever for energy harvesting, sensing, and actuation. Nonlinear Dyn 79:1727–1743
Bisplinghoff RL, Ashley H, Halfman RL (1962) Principles Aeroelasticity. John Wiley & Sons, New York
Dimitriadis G (2017) Intro onlinear Aeroelasticity. John Wiley & Sons, New York
Edwards JW, Ashley H, Breakwell JV (1979) Unsteady aerodynamic modeling for arbitrary motions. AIAA J 17:365–374
Nayfeh AH, Balachandran B (2008) Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. John Wiley & Sons, New York
Ghommem M, Nayfeh A.H, Hajj M.R (2010) Control of limit cycle oscillations of a two-dimensional aeroelastic system. Math Prob Eng. 2010
Sanches L, Guimarães TAM, Marques FD (2019) Aeroelastic tailoring of nonlinear typical section using the method of multiple scales to predict post-flutter stable lcos. Aerosp Sci Technol 90:157–168
Acknowledgements
ACGA thanks CAPES (grant #88887.606139/2021-00) and MS thanks CNPq (grant #309860/2020-2) for financial support for this project.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that there are no competing interests.
Additional information
Technical Editor: Pedro Manuel Calas Lopes Pacheco.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Amaral, A.C.G., De Marqui, C. & Silveira, M. Aeroelastic energy harvesting in flutter condition increases with combined nonlinear stiffness and nonlinear piezoelectrical coupling. J Braz. Soc. Mech. Sci. Eng. 45, 111 (2023). https://doi.org/10.1007/s40430-023-04028-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-023-04028-w