Technical Papers
May 19, 2023

Nonlinear Dynamics of a Broadband Vortex-Induced Vibration–Based Energy Harvester

Publication: Journal of Engineering Mechanics
Volume 149, Issue 8

Abstract

Energy harvesting from vortex-induced vibrations (VIV) is gaining more attention in many applied cases. This paper studied the nonlinear dynamics of a tunable VIV-based energy harvester. The energy harvester structure consists of a base-clamped cylinder having an adjustable mass (the tuner) which enables the system to actively synchronize with vortex-shedding frequencies. The Euler-Bernoulli beam theory and the extended Hamilton’s principle are used to extract the nonlinear partial differential equations of the distributed model for the cylinder, tuner motion, harvested voltage, and fluctuated lift force. The reduced-order model of the system of equations is derived via the Galerkin method using modified mode shapes. The method of multiple time scales is employed to obtain the approximated analytical solution of the 1:1 internal resonance of the lumped parameter system. The dynamical response of the system is shown by investigating various parameters of the harvester. Additionally, the locus of the points at which the higher orbits of harvested voltage occur is specified for the tuner equilibrium position. The results show the proposed design significantly increases energy harvesting performance by a factor of 900%. This paper is offered as a contribution towards energy harvester design and optimization with the goal of capturing higher energy orbits.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The authors gratefully acknowledge the support provided by Eng. Kamran Soltani, CEO of Novin Sanat Eghtesad Gostar Fartak (NSEGF) company.

References

Abdelkefi, A., M. R. Hajj, and A. H. Nayfeh. 2012a. “Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders.” Nonlinear Dyn. 70 (2): 1377–1388. https://doi.org/10.1007/s11071-012-0540-x.
Abdelkefi, A., M. R. Hajj, and A. H. Nayfeh. 2012b. “Power harvesting from transverse galloping of square cylinder.” Nonlinear Dyn. 70 (2): 1355–1363. https://doi.org/10.1007/s11071-012-0538-4.
Abdelkefi, A., A. H. Nayfeh, and M. R. Hajj. 2012c. “Modeling and analysis of piezoaeroelastic energy harvesters.” Nonlinear Dyn. 67 (2): 925–939. https://doi.org/10.1007/s11071-011-0035-1.
Akaydin, H. D., N. Elvin, and Y. Andreopoulos. 2012. “The performance of a self-excited fluidic energy harvester.” Smart Mater. Struct. 21 (2): 025007. https://doi.org/10.1088/0964-1726/21/2/025007.
Besem, F. M., J. D. Kamrass, J. P. Thomas, D. Tang, and R. E. Kielb. 2016. “Vortex-induced vibration and frequency lock-in of an airfoil at high angles of attack.” J. Fluids Eng. 138 (1): 1–9. https://doi.org/10.1115/1.4031134.
Blevins, R. D. 1990. Flow-induced vibrations. New York: Van Nostrand Reinhold.
Bryant, M., and E. Garcia. 2011. “Modeling and testing of a novel aeroelastic flutter energy harvester.” J. Vib. Acoust. 133 (1): 011010. https://doi.org/10.1115/1.4002788.
Chen, J., and Q. S. Li. 2019. “Nonlinear dynamics of a fluid-structure coupling model for vortex-induced vibration.” Int. J. Struct. Stab. Dyn. 19 (7): 1950071. https://doi.org/10.1142/S0219455419500718.
Chen, S.-S. 1985. Flow-induced vibration of circular cylindrical structures. By Chen 1985.pdf. Argonne, IL: Argonne National Lab.
Chizfahm, A., E. A. Yazdi, and M. Eghtesad. 2018. “Dynamic modeling of vortex induced vibration wind turbines.” Renewable Energy 121 (Jun): 632–643. https://doi.org/10.1016/j.renene.2018.01.038.
Dai, H. L., L. Wang, Q. Qian, and Q. Ni. 2014. “Vortex-induced vibrations of pipes conveying pulsating fluid.” Ocean Eng. 77 (Feb): 12–22. https://doi.org/10.1016/j.oceaneng.2013.12.006.
Daqaq, M. F., R. Masana, A. Erturk, and D. D. Quinn. 2014. “On the role of nonlinearities in vibratory energy harvesting: A critical review and discussion.” Appl. Mech. Rev. 66 (4): 040801. https://doi.org/10.1115/1.4026278.
De Marqui, C., W. G. R. Vieira, A. Erturk, and D. J. Inman. 2011. “Modeling and analysis of piezoelectric energy harvesting from aeroelastic vibrations using the doublet-lattice method.” J. Vib. Acoust. 133 (1): 011003. https://doi.org/10.1115/1.4002785.
Eichhorn, C., R. Tchagsim, N. Wilhelm, and P. Woias. 2011. “A smart and self-sufficient frequency tunable vibration energy harvester.” J. Micromech. Microeng. 21 (10): 104003. https://doi.org/10.1088/0960-1317/21/10/104003.
Erturk, A., W. G. R. Vieira, C. De Marqui, and D. J. Inman. 2010. “On the energy harvesting potential of piezoaeroelastic systems.” Appl. Phys. Lett. 96 (18): 184103. https://doi.org/10.1063/1.3427405.
Facchinetti, M. L., E. de Langre, and F. Biolley. 2004. “Coupling of structure and wake oscillators in vortex-induced vibrations.” J. Fluids Struct. 19 (2): 123–140. https://doi.org/10.1016/j.jfluidstructs.2003.12.004.
Foisal, A. R. M., C. Hong, and G. S. Chung. 2012. “Multi-frequency electromagnetic energy harvester using a magnetic spring cantilever.” Sens. Actuators, A 182 (Aug): 106–113. https://doi.org/10.1016/j.sna.2012.05.009.
Gupta, S. K., A. L. Malla, and O. R. Barry. 2021. “Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers.” Nonlinear Dyn. 103 (1): 27–47. https://doi.org/10.1007/s11071-020-06100-9.
Harne, R. L., and K. W. Wang. 2013. “A review of the recent research on vibration energy harvesting via bistable systems.” Smart Mater. Struct. 22 (2): 23001. https://doi.org/10.1088/0964-1726/22/2/023001.
Heydari, S., N. A. Patankar, M. J. Z. Hartmann, and R. K. Jaiman. 2021. “On the fluid-structure interaction of a flexible cantilever cylinder at low Reynolds numbers.” Preprint, submitted May 25, 2021. https://arxiv.org/abs/2105.11663.
Hoskoti, L., A. Misra, and M. M. Sucheendran. 2018. “Frequency lock-in during vortex induced vibration of a rotating blade.” J. Fluids Struct. 80 (Jul): 145–164. https://doi.org/10.1016/j.jfluidstructs.2018.03.011.
Hsu, J., C. Tseng, and Y. Chen. 2014. “Analysis and experiment of self-frequency-tuning piezoelectric energy harvesters for rotational motion.” Smart Mater. Struct. 23 (7): 075013. https://doi.org/10.1088/0964-1726/23/7/075013.
Hu, G., K. T. Tse, K. C. S. Kwok, J. Song, and Y. Lyu. 2016. “Aerodynamic modification to a circular cylinder to enhance the piezoelectric wind energy harvesting.” Appl. Phys. Lett. 109 (19): 1–6. https://doi.org/10.1063/1.4967497.
Hu, G., K. T. Tse, M. Wei, R. Naseer, A. Abdelkefi, and K. C. S. Kwok. 2018. “Experimental investigation on the efficiency of circular cylinder-based wind energy harvester with different rod-shaped attachments.” Appl. Energy 226 (Jun): 682–689. https://doi.org/10.1016/j.apenergy.2018.06.056.
Karadag, C. V., and N. Topaloglu. 2017. “A self-sufficient and frequency tunable piezoelectric vibration energy harvester.” J. Vib. Acoust. 139 (1): 1–8. https://doi.org/10.1115/1.4034775.
Kim, P., Y. J. Yoon, and J. Seok. 2016. “Nonlinear dynamic analyses on a magnetopiezoelastic energy harvester with reversible hysteresis.” Nonlinear Dyn. 83 (4): 1823–1854. https://doi.org/10.1007/s11071-015-2449-7.
Kurushina, V., A. Postnikov, G. Franzini, and E. Pavlovskaia. 2022. “Optimization of the wake oscillator for transversal VIV.” J. Mar. Sci. Eng. 10 (2): 293. https://doi.org/10.3390/jmse10020293.
Liu, H., and X. Gao. 2019. “Vibration energy harvesting under concurrent base and flow excitations with internal resonance.” Nonlinear Dyn. 96 (2): 1067–1081. https://doi.org/10.1007/s11071-019-04839-4.
Liu, H., Y. Qian, and C. Lee. 2013. “A multi-frequency vibration-based MEMS electromagnetic energy harvesting device.” Sens. Actuators, A 204 (Dec): 37–43. https://doi.org/10.1016/j.sna.2013.09.015.
Maamer, B., A. Boughamoura, A. M. R. Fath El-Bab, L. A. Francis, and F. Tounsi. 2019. “A review on design improvements and techniques for mechanical energy harvesting using piezoelectric and electromagnetic schemes.” Energy Convers. Manage. 199 (Feb): 111973. https://doi.org/10.1016/j.enconman.2019.111973.
Mehmood, A., A. Abdelkefi, M. R. Hajj, A. H. Nayfeh, I. Akhtar, and A. O. Nuhait. 2013. “Piezoelectric energy harvesting from vortex-induced vibrations of circular cylinder.” J. Sound Vib. 332 (19): 4656–4667. https://doi.org/10.1016/j.jsv.2013.03.033.
Miller, L. M., P. Pillatsch, E. Halvorsen, P. K. Wright, E. M. Yeatman, and A. S. Holmes. 2013. “Experimental passive self-tuning behavior of a beam resonator with sliding proof mass.” J. Sound Vib. 332 (26): 7142–7152. https://doi.org/10.1016/j.jsv.2013.08.023.
Naseer, R., H. L. Dai, A. Abdelkefi, and L. Wang. 2017. “Piezomagnetoelastic energy harvesting from vortex-induced vibrations using monostable characteristics.” Appl. Energy 203 (Oct): 142–153. https://doi.org/10.1016/j.apenergy.2017.06.018.
Navrose, N., and S. Mittal. 2016. “Lock-in in vortex-induced vibration.” J. Fluid Mech. 794 (May): 565–594. https://doi.org/10.1017/jfm.2016.157.
Nayfeh, A. H., and D. T. Mook. 2008. Nonlinear oscillations. New York: Wiley.
Nguyen, M. S., Y. J. Yoon, and P. Kim. 2019. “Enhanced broadband performance of magnetically coupled 2-DOF bistable energy harvester with secondary intrawell resonances.” Int. J. Precis. Eng. Manuf. Green Technol. 6 (3): 521–530. https://doi.org/10.1007/s40684-019-00048-x.
Nishi, Y., and K. Saitoh. 2017. “Vortex-induced vibration of two elastically connected bodies: Experimental verification of lock-in to multiple eigenmodes.” J. Fluid Sci. Technol. 12 (2): JFST0016. https://doi.org/10.1299/jfst.2017jfst0016.
Rostami, A. B., and M. Armandei. 2017. “Renewable energy harvesting by vortex-induced motions: Review and benchmarking of technologies.” Renewable Sustainable Energy Rev. 70 (Jun): 193–214. https://doi.org/10.1016/j.rser.2016.11.202.
Sari, I., T. Balkan, and H. Kulah. 2008. “An electromagnetic micro power generator for wideband environmental vibrations.” Sens. Actuators, A 145–146 (1–2): 405–413. https://doi.org/10.1016/j.sna.2007.11.021.
Seyed-Aghazadeh, B., H. Samandari, and S. Dulac. 2020. “Flow-induced vibration of inherently nonlinear structures with applications in energy harvesting.” Phys. Fluids (1994) 32 (7): 071701. https://doi.org/10.1063/5.0012247.
Siddiqui, S. A. Q., M. F. Golnaraghi, and G. R. Heppler. 1998. “Dynamics of a flexible cantilever beam carrying a moving mass.” Nonlinear Dyn. 15 (2): 137–154. https://doi.org/10.1023/A:1008205904691.
Siddiqui, S. A. Q., M. F. Golnaraghi, and G. R. Heppler. 2000. “Dynamics of a flexible beam carrying a moving mass using perturbation, numerical and time-frequency analysis techniques.” J. Sound Vib. 229 (5): 1023–1055. https://doi.org/10.1006/jsvi.1999.2449.
Skop, R. A., and S. Balasubramanian. 1997. “A new twist on an old model for vortex-excited vibrations.” J. Fluids Struct. 11 (4): 395–412. https://doi.org/10.1006/jfls.1997.0085.
Skop, R. A., and O. M. Griffin. 1975. “On a theory for the vortex-excited.” J. Sound Vib. 41 (3): 263–274. https://doi.org/10.1016/S0022-460X(75)80173-8.
Soltani, K., and G. Rezazadeh. 2022. “Wide range tuning behavior of a new non-linear energy harvester based on the beam-slider structure.” Arch. Appl. Mech. 92 (10): 3013–3031. https://doi.org/10.1007/s00419-022-02223-0.
Sun, W., F. Guo, and J. Seok. 2019. “Development of a novel vibro-wind galloping energy harvester with high power density incorporated with a nested bluff-body structure.” Energy Convers. Manage. 197 (Oct): 111880. https://doi.org/10.1016/j.enconman.2019.111880.
Sun, W., J. Jung, and J. Seok. 2016. “Frequency-tunable electromagnetic energy harvester using magneto-rheological elastomer.” J. Intell. Mater. Syst. Struct. 27 (7): 959–979. https://doi.org/10.1177/1045389X15590274.
Sun, W., J. Jung, X. Y. Wang, P. Kim, J. Seok, and D. Y. Jang. 2015. “Design, simulation, and optimization of a frequency-tunable vibration energy harvester that uses a magnetorheological elastomer.” Adv. Mech. Eng. 7 (1): 147421. https://doi.org/10.1155/2014/147421.
Sun, W., and J. Seok. 2020. “A novel self-tuning wind energy harvester with a slidable bluff body using vortex-induced vibration.” Energy Convers. Manage. 205 (Feb): 112472. https://doi.org/10.1016/j.enconman.2020.112472.
Toyabur, R. M., M. Salauddin, H. Cho, and J. Y. Park. 2018. “A multimodal hybrid energy harvester based on piezoelectric-electromagnetic mechanisms for low-frequency ambient vibrations.” Energy Convers. Manage. 168 (Apr): 454–466. https://doi.org/10.1016/j.enconman.2018.05.018.
Viré, A., A. Derksen, M. Folkersma, and K. Sarwar. 2019. “Two-dimensional numerical simulations of vortex-induced vibrations for wind turbine towers.” Wind Energy Sci. Discuss. 2019 (Dec): 1–19. https://doi.org/10.5194/wes-2019-83.
Wang, J., S. Zhou, Z. Zhang, and D. Yurchenko. 2019. “High-performance piezoelectric wind energy harvester with Y-shaped attachments.” Energy Convers. Manage. 181 (Dec): 645–652. https://doi.org/10.1016/j.enconman.2018.12.034.
Wang, Y., Z. Wu, G. Zhang, Y. Li, and F. Wang. 2020. “Bifurcation phenomenon and multi-stable behavior in vortex-induced vibration of top tension riser in shear flow.” J. Vib. Control 26 (9–10): 659–670. https://doi.org/10.1177/1077546319889856.
Williamson, C. H. K., and R. Govardhan. 2004. “Vortex-induced vibrations.” Annu. Rev. Fluid Mech. 36 (1): 413–455. https://doi.org/10.1146/annurev.fluid.36.050802.122128.
Yang, Y., L. Zhao, and L. Tang. 2013. “Comparative study of tip cross-sections for efficient galloping energy harvesting.” Appl. Phys. Lett. 102 (6): 64105. https://doi.org/10.1063/1.4792737.
Yu, L., L. Tang, and T. Yang. 2020. “Piezoelectric passive self-tuning energy harvester based on a beam-slider structure.” J. Sound Vib. 489 (Dec): 115689. https://doi.org/10.1016/j.jsv.2020.115689.
Zhang, L. B., A. Abdelkefi, H. L. Dai, R. Naseer, and L. Wang. 2017. “Design and experimental analysis of broadband energy harvesting from vortex-induced vibrations.” J. Sound Vib. 408 (Nov): 210–219. https://doi.org/10.1016/j.jsv.2017.07.029.
Zhang, L. B., H. L. Dai, A. Abdelkefi, and L. Wang. 2019. “Experimental investigation of aerodynamic energy harvester with different interference cylinder cross-sections.” Energy 167 (Jan): 970–981. https://doi.org/10.1016/j.energy.2018.11.059.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 149Issue 8August 2023

History

Received: Aug 8, 2022
Accepted: Mar 6, 2023
Published online: May 19, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 19, 2023

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Kamran Soltani [email protected]
Engineer, Dept. of Mechanical Engineering, Urmia Univ., Urmia, West Azerbaijan 5773119655, Iran (corresponding author). Email: [email protected]
Professor, Dept. of Mechanical Engineering, Urmia Univ., Urmia, West Azerbaijan 5719916589, Iran; Dept. of Engineering, South Ural State Univ., Chelyabinsk, Russia. ORCID: https://orcid.org/0000-0001-5243-3199. Email: [email protected]
Professor, Fluids and Complex Systems Centre, Univ. of Coventry, Priory St., Coventry CV1 5FB, UK; Dept. of Engineering Science, Univ. of Oxford, Parks Rd., Oxford OX1 3PJ, UK. ORCID: https://orcid.org/0000-0002-9677-1234. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share