[en] An electromechanical model for beam-like piezoelectric energy harvesters based on Reissner’s beam theory is developed in this paper. The proposed model captures first-order shear deformation and large displacement/rotation, which distinguishes this model from other models reported in the literature. All governing equations are presented in detail, making the associated framework extensible to investigate various piezoelectric energy harvesters. The weak formulation is then derived to obtain the approximate solution to the governing equations by the finite element method. This solution scheme is completely coupled, and thus allows for two-way interaction between mechanical and electrical fields. To validate this model, extensive numerical examples are implemented in the linear and nonlinear regime. In the linear limit, this model produces results in excellent agreement with reference data. In the nonlinear regime, the large amplitude response of the piezoelectric beam induced by strong base excitation or fluid flow is considered, and the comparison of results with literature data is encouraging. The ability of this nonlinear model to predict limit cycle oscillations in axial flow is demonstrated.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
SHANG, Lan ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Hoareau, Christophe; Conservatoire national des arts et métiers (Cnam) > Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC)
ZILIAN, Andreas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
External co-authors :
yes
Language :
English
Title :
A geometrically nonlinear shear deformable beam model for piezoelectric energy harvesters
Publication date :
2021
Journal title :
Acta Mechanica
ISSN :
0001-5970
eISSN :
1619-6937
Publisher :
Springer, Vienna, Germany
Volume :
232
Issue :
12
Pages :
4847-4866
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
FnR Project :
FNR12252781 - Data-driven Computational Modelling And Applications, 2017 (01/09/2018-28/02/2025) - Andreas Zilian
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Hwang, W.S., Park, H.C.: Finite element modeling of piezoelectric sensors and actuators. AIAA J. 31(5), 930–937 (1993) DOI: 10.2514/3.11707
Krommer, M., Irschik, H.: An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics. Acta Mech. 154(1), 141–158 (2002) DOI: 10.1007/BF01170704
Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18(2), 025009 (2009) DOI: 10.1088/0964-1726/18/2/025009
Bibo, A., Abdelkefi, A., Daqaq, M.F.: Modeling and characterization of a piezoelectric energy harvester under combined aerodynamic and base excitations. J. Vibrat. Acoust. 137(3), 031017 (2015) DOI: 10.1115/1.4029611
Fu, H., Chen, G., Bai, N.: Electrode coverage optimization for piezoelectric energy harvesting from tip excitation. Sensors 18(3), 804 (2018) DOI: 10.3390/s18030804
Amini, Y., Emdad, H., Farid, M.: An accurate model for numerical prediction of piezoelectric energy harvesting from fluid structure interaction problems. Smart Mater. Struct. 23(9), 095034 (2014) DOI: 10.1088/0964-1726/23/9/095034
Orrego, S., Shoele, K., Ruas, A., Doran, K., Caggiano, B., Mittal, R., Kang, S.H.: Harvesting ambient wind energy with an inverted piezoelectric flag. Appl. Energy 194, 212–222 (2017) DOI: 10.1016/j.apenergy.2017.03.016
De Marqui Jr, C., Tan, D., Erturk, A.: On the electrode segmentation for piezoelectric energy harvesting from nonlinear limit cycle oscillations in axial flow. J. Fluids Struct. 82, 492–504 (2018) DOI: 10.1016/j.jfluidstructs.2018.07.020
Ravi, S., Zilian, A.: Simultaneous finite element analysis of circuit-integrated piezoelectric energy harvesting from fluid-structure interaction. Mech. Syst. Signal Process. 114, 259–274 (2019) DOI: 10.1016/j.ymssp.2018.05.016
Dunnmon, J., Stanton, S., Mann, B., Dowell, E.: Power extraction from aeroelastic limit cycle oscillations. J. Fluids Struct. 27(8), 1182–1198 (2011) DOI: 10.1016/j.jfluidstructs.2011.02.003
Roundy, S., Wright, P.K.: A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct. 13(5), 1131 (2004) DOI: 10.1088/0964-1726/13/5/018
Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vibr. Acoust. 130(4), (2008)
Erturk, A., Inman, D.J.: Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. 17(6), 065016 (2008) DOI: 10.1088/0964-1726/17/6/065016
Erturk, A.: Assumed-modes modeling of piezoelectric energy harvesters: Euler-Bernoulli, Rayleigh, and Timoshenko models with axial deformations. Comput. Struct. 106, 214–227 (2012) DOI: 10.1016/j.compstruc.2012.05.010
Dietl, J., Wickenheiser, A., Garcia, E.: A Timoshenko beam model for cantilevered piezoelectric energy harvesters. Smart Mater. Struct. 19(5), 055018 (2010) DOI: 10.1088/0964-1726/19/5/055018
Zhu, Y., Zu, J.W., Yao, M.: In ASME 2011 conference on smart materials, adaptive structures and intelligent systems (American Society of Mechanical Engineers Digital Collection), pp. 115–122 (2011)
Zhao, X., Yang, E., Li, Y., Crossley, W.: Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions. J. Intell. Mater. Syst. Struct. 28(17), 2372–2387 (2017) DOI: 10.1177/1045389X17689927
Tang, D., Zhao, M., Dowell, E.H.: Inextensible beam and plate theory: computational analysis and comparison with experiment. J. Appl. Mech. 81(6), (2014)
Tang, D., Dowell, E.H.: Limit cycle oscillations of two-dimensional panels in low subsonic flow. Int. J. Non-Linear Mech. 37(7), 1199–1209 (2002) DOI: 10.1016/S0020-7462(01)00140-8
Semler, C., Li, G.X., Paıdoussis, M.: The non-linear equations of motion of pipes conveying fluid. J. Sound Vib. 169(5), 577–599 (1994) DOI: 10.1006/jsvi.1994.1035
Lumentut, M., Howard, I.: Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations. Smart Mater. Struct. 23(9), 095037 (2014) DOI: 10.1088/0964-1726/23/9/095037
Elvin, N.G., Elvin, A.A.: Large deflection effects in flexible energy harvesters. J. Intell. Mater. Syst. Struct. 23(13), 1475–1484 (2012) DOI: 10.1177/1045389X11435434
Ravi, S., Zilian, A.: Monolithic modeling and finite element analysis of piezoelectric energy harvesters. Acta Mech. 228(6), 2251–2267 (2017) DOI: 10.1007/s00707-017-1830-7
Reissner, E.: On one-dimensional finite-strain beam theory: the plane problem. Zeitschrift für angewandte Mathematik und Physik ZAMP 23(5), 795–804 (1972) DOI: 10.1007/BF01602645
Ortigosa, R., Gil, A.J., Bonet, J., Hesch, C.: A computational framework for polyconvex large strain elasticity for geometrically exact beam theory. Comput. Mech. 57(2), 277–303 (2016) DOI: 10.1007/s00466-015-1231-5
Humer, A., Krommer, M.: Modeling of piezoelectric materials by means of a multiplicative decomposition of the deformation gradient. Mech. Adv. Mater. Struct. 22(1–2), 125–135 (2015) DOI: 10.1080/15376494.2014.907948
Auricchio, F., Carotenuto, P., Reali, A.: On the geometrically exact beam model: a consistent, effective and simple derivation from three-dimensional finite-elasticity. Int. J. Solids Struct. 45(17), 4766–4781 (2008) DOI: 10.1016/j.ijsolstr.2008.04.015
Erturk, A., Inman, D.J.: Piezoelectric Energy Harvesting, pp. 345–346. Wiley, Hoboken (2011) DOI: 10.1002/9781119991151
Stanton, S.C., Erturk, A., Mann, B.P., Inman, D.J.: Nonlinear piezoelectricity in electroelastic energy harvesters: modeling and experimental identification. J. Appl. Phys. 108(7), 074903 (2010) DOI: 10.1063/1.3486519
Gherlone, M.: On the use of zigzag functions in equivalent single layer theories for laminated composite and sandwich beams: a comparative study and some observations on external weak layers. J. Appl. Mech. 80(6), (2013)
Erturk, A., Tarazaga, P.A., Farmer, J.R., Inman, D.J.: Effect of strain nodes and electrode configuration on piezoelectric energy harvesting from cantilevered beams. J. Vibr. Acoust. 131(1), (2009)
Schoeftner, J., Irschik, H.: A comparative study of smart passive piezoelectric structures interacting with electric networks: Timoshenko beam theory versus finite element plane stress calculations. Smart Mater. Struct. 20(2), 025007 (2011) DOI: 10.1088/0964-1726/20/2/025007
Gatti, C.D., Febbo, M., Machado, S.P., Osinaga, S.: A piezoelectric beam model with geometric, material and damping nonlinearities for energy harvesting. Smart Mater. Struct. (2020)
de Carvalho Dias, J.A., de Sousa, V.C., Erturk, A., Carlos Jr, D.M.: Nonlinear piezoelectric plate framework for aeroelastic energy harvesting and actuation applications. Smart Mater. Struct. (2020)
Fenics project. https://fenicsproject.org/
Logg, A., Mardal, K.A., Wells, G.: Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, vol. 84. Springer, Berlin (2012) DOI: 10.1007/978-3-642-23099-8
Chung, J., Hulbert, G.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- α method (1993)
Elvin, N.G., Elvin, A.A.: A coupled finite element-circuit simulation model for analyzing piezoelectric energy generators. J. Intell. Mater. Syst. Struct. 20(5), 587–595 (2009) DOI: 10.1177/1045389X08101565
Fallahpasand, S., Dardel, M.: Piezoelectric energy harvesting from highly flexible cantilever beam. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn. 233(1), 71–92 (2019)
Farokhi, H., Ghayesh, M.H.: Geometrically exact extreme vibrations of cantilevers. Int. J. Mech. Sci. 168, 105051 (2020) DOI: 10.1016/j.ijmecsci.2019.105051
Eloy, C., Kofman, N., Schouveiler, L.: The origin of hysteresis in the flag instability. J. Fluid Mech. 691, 583–593 (2012) DOI: 10.1017/jfm.2011.494
Howell, J.S., Toundykov, D., Webster, J.T.: A cantilevered extensible beam in axial flow: semigroup well-posedness and postflutter regimes. SIAM J. Math. Anal. 50(2), 2048–2085 (2018) DOI: 10.1137/17M1140261
Madabhusi-Raman, P., Davalos, J.F.: Static shear correction factor for laminated rectangular beams. Compos. B Eng. 27(3–4), 285–293 (1996) DOI: 10.1016/1359-8368(95)00014-3
Similar publications
Sorry the service is unavailable at the moment. Please try again later.