This paper investigates electromagnetic energy harvesting based on vibration energy extraction from the vibration of a bluff body elastically connected with an additional nonlinear oscillator and subjected to fluid flow and base excitation. The mechanical part is modeled as a system of two coupled oscillators where a combination of harmonic base excitation and fluid forces leads to a steady-state regime. The electromagnetic generator as part of the harvesting device is represented by the equivalent electrical circuit with power dissipated at an electrical load resistance. The mathematical model is based on a set of two coupled nonlinear ordinary differential equations considering the transverse displacement of a bluff body, additional nonlinear oscillator, and currents induced in the electromagnetic generator. By introducing the incremental harmonic balance and continuation methods nonlinear periodic responses are investigated and complex dynamic behavior presented through corresponding response diagrams. The results indicate that for some values of system parameters multiple periodic solutions appear in the form of loops and hysteresis. Finally, the average power of proposed energy harvester is given in time history diagrams for different values of nonlinear stiffness parameter and velocity of fluid flow.
NakamuraTKanekoSInadaF, et al. (eds) Flow-induced vibrations: classifications and lessons from practical experiences.
Butterworth-Heinemann, 2013.
2.
LiDWuYDa RonchA, et al.
Energy harvesting by means of flow-induced vibrations on aerospace vehicles. Progr Aerosp Sci2016;
86: 28–62.
3.
AbdelkefiA.Aeroelastic energy harvesting: a review. Int J Eng Sci2016;
100: 112–135.
4.
AbdelkefiAHajjMRNayfehAH.Piezoelectric energy harvesting from transverse galloping of bluff bodies. Smart Mater Struct2013;
22: 015014.
5.
AbdelkefiAYanZHajjMR.Modeling and nonlinear analysis of piezoelectric energy harvesting from transverse galloping. Smart Mater Struct2013;
22: 025016.
6.
AbdelkefiAHajjMRNayfehAH.Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders. Nonlinear Dyn2012;
70: 1377–1388.
7.
DaiHLAbdelmoulaHAbdelkefiA, et al.
Towards control of cross-flow-induced vibrations based on energy harvesting. Nonlinear Dyn2017;
88: 2329–2346.
8.
DaiHLAbdelkefiAWangL.Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations. Nonlinear Dyn2014;
77: 967–981.
9.
DaiHLAbdelkefiAJavedU, et al.
Modeling and performance of electromagnetic energy harvesting from galloping oscillations. Smart Mater Struct2015;
24: 045012.
10.
Vicente-LudlamDBarrero-GilAVelazquezA.Optimal electromagnetic energy extraction from transverse galloping. J Fluids Struct2014;
51: 281–291.
11.
DaiHLYangYWAbdelkefiA, et al.
Nonlinear analysis and characteristics of inductive galloping energy harvesters. Commun Nonlinear Sci Numer Simul2018;
59: 580–591.
12.
PennisiGMannBPNaclerioN, et al.
Design and experimental study of a nonlinear energy sink coupled to an electromagnetic energy harvester. J Sound Vibr2018;
437: 340–357.
13.
LiuHGaoX.Vibration energy harvesting under concurrent base and flow excitations with internal resonance. Nonlinear Dyn2019;
96: 1067–1081.
14.
De MarquiCJrErturkA.Electroaeroelastic analysis of airfoil-based wind energy harvesting using piezoelectric transduction and electromagnetic induction. J Intell Mater Syst Struct2013;
24: 846–854.
15.
DiasJACDe MarquiCJrErturkA.Three-degree-of-freedom hybrid piezoelectric-inductive aeroelastic energy harvester exploiting a control surface. AIAA J2015;
53: 394–404.
16.
BiboADaqaqMF.Energy harvesting under combined aerodynamic and base excitations. J Sound Vibr2013;
332: 5086–5102.
17.
DaqaqMFBiboAAkhtarI, et al.
Micropower generation using cross-flow instabilities: a review of the literature and its implications. J Vibr Acoust2019;
141: 030801.
18.
VakakisAFGendelmanOVBergmanLA, et al.Nonlinear targeted energy transfer in mechanical and structural systems (vol.
156).
New York:
Springer Science & Business Media, 2008.
19.
VakakisAF.Passive nonlinear targeted energy transfer. Phil Trans R Soc A2018;
376: 20170132.
20.
GendelmanOManevitchLIVakakisAF, et al.
Energy pumping in nonlinear mechanical oscillators: part I—dynamics of the underlying Hamiltonian systems. J Appl Mech2001;
68: 34–41.
21.
TumkurRKRDomanyEGendelmanOV, et al.
Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber. Commun Nonlinear Sci Numer Simul2013;
18: 1916–1930.
22.
BlanchardABergmanLAVakakisAF.Vortex-induced vibration of a linearly sprung cylinder with an internal rotational nonlinear energy sink in turbulent flow. Nonlinear Dyn2020;
99: 593–517.
23.
DaiHLAbdelkefiAWangL.Usefulness of passive non-linear energy sinks in controlling galloping vibrations. I J Nonlinear Mech2016;
81: 83–94.
24.
DaiHLAbdelkefiAWangL.Vortex-induced vibrations mitigation through a nonlinear energy sink. Commun Nonlinear Sci Numer Simul2017;
42: 22–36.
25.
ZhangYTangLLiuK.Piezoelectric energy harvesting with a nonlinear energy sink. J Intell Mater Syst Struct2017;
28: 307–322.
26.
KremerDLiuK.A nonlinear energy sink with an energy harvester: transient responses. J Sound Vibr2014;
333: 4859–4880.
27.
TangXZuoL.Enhanced vibration energy harvesting using dual-mass systems. J Sound Vibr2011;
330: 5199–5209.
28.
NishiY.Power extraction from vortex-induced vibration of dual mass system. J Sound Vibr2013;
332: 199–212.
29.
Vicente-LudlamDBarrero-GilAVelazquezA.Enhanced mechanical energy extraction from transverse galloping using a dual mass system. J Sound Vibr2015;
339: 290–303.
30.
JavedUAbdelkefiAAkhtarI.An improved stability characterization for aeroelastic energy harvesting applications. Commun Nonlinear Sci Numer Simul2016;
36: 252–265.
31.
BlevinsRD.Flow-induced vibration.
Van Nostrand Reinhold.
New York, 1990.
32.
El-HamiMGlynne-JonesPWhiteNM, et al.
Design and fabrication of a new vibration-based electromechanical power generator. Sens Actuat A Phys2001;
92: 335–342.
33.
DouSJensenJS.Optimization of nonlinear structural resonance using the incremental harmonic balance method. J Sound Vibr2015;
334: 239–254.
34.
FuYMZhangJBiRG.Analysis of the nonlinear dynamic stability for an electrically actuated viscoelastic microbeam. Microsyst Technol2009;
15: 763–769.
35.
KongXLiHWuC.Dynamics of 1-dof and 2-dof energy sink with geometrically nonlinear damping: application to vibration suppression. Nonlinear Dyn2018;
91: 733–754.
36.
ZhouSSongGLiY, et al.
Dynamic and steady analysis of a 2-DOF vehicle system by modified incremental harmonic balance method. Nonlinear Dyn2019;
98: 75–94.
37.
LeungAYTChuiSK.Non-linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method. J Sound Vibr1995;
181: 619–633.
38.
BhattiproluUBajajAKDaviesP.Periodic response predictions of beams on nonlinear and viscoelastic unilateral foundations using incremental harmonic balance method. Int J Solids Struct2016;
99: 28–39.
39.
HuangJLSuRKLLeeYY, et al.
Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities. J Sound Vibr2011;
330: 5151–5164.
40.
WangSHuaLYangC, et al.
Applications of incremental harmonic balance method combined with equivalent piecewise linearization on vibrations of nonlinear stiffness systems. J Sound Vibr2019;
441: 111–125.
41.
SeydelR.2009. Practical bifurcation and stability analysis (vol.
5).
New York:
Springer Science & Business Media.
42.
NollMULentzLvon WagnerU.On the discretization of a bistable cantilever beam with application to energy harvesting. FU Mech Eng2019;
17: 125–139.
43.
Noll MU, Lentz L and von Wagner U. On the improved modeling of the magnetoelastic force in a vibrational energy harvesting system. Journal of Vibration Engineering & Technologies 2020; 8: 285–295.
44.
WangDAChangKH.Electromagnetic energy harvesting from flow-induced vibration. Microelectron J2010;
41: 356–364.
45.
MalatkarPNayfehAH.Steady-state dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator. Nonlinear Dyn2006;
47: 167–179.
46.
DaqaqMFMasanaRErturkA, et al.
On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. Appl Mech Rev2014;
66
