Nonlinear Piezoelectric Model for Circular Plates: Influence of Geometric and Material Nonlinearity
DOI:
https://doi.org/10.70567/mc.v42.ocsid8203Keywords:
Energy harvesting, piezoelectricity, vibrationAbstract
A nonlinear model for circular plate piezoelectric collectors is presented based on the classical Von-Karman plate theory that captures nonlinear phenomena associated with large displacements. The model incorporates the nonlinearity of constitutive electromechanical coupling, the constitutive nonlinearity of the piezoelectric material, and dissipation nonlinearities. The harvester has an oscillating mass attached for improved energy extraction and tuning to a given resonant frequency. Geometric nonlinearity is derived from the stress function known as the Airy function and is solved analytically to be incorporated into the plate's transverse equilibrium equation. This article analyzes the influence of geometric nonlinearity determined by this formulation for large accelerations. Results between approximate and exact formulations are compared with experimental test results. The study is carried out on an energy harvester whose resonant frequency is around 141 Hz.
References
Abdelkefi A, Nayfeh A, and Hajj M. "Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation," Nonlinear Dynamics”,vol. 67, pp. 1221-1232, 2012. https://doi.org/10.1007/s11071-011-0064-9
Amabili, M. Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press. United Kingdom, 2008.
Chen X R, Yang T Q, Wang W and Yao X. Vibration energy harvesting with a clamped piezoelectric circular diaphragm. Ceram. Int. 38 S271–4, 2012. https://doi.org/10.1016/j.ceramint.2011.04.099
Erturk A. and Imnan D. J. An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Materials and Structures, 18(2), 2009. https://doi.org/10.1088/0964-1726/18/2/025009
Erturk A. and Inman D. J. Piezoelectric Energy Harvesting. Wiley, Chichester, United Kingdom, 2011. https://doi.org/10.1002/9781119991151.ch10
Faris Waleed F. Nonlinear Dynamics of Annular and Circular Plates under Thermal and Electrical Loadings. Dissertation submitted to the Faculty of the Engineering Virginia Polytechnic Institute and State University in partial fulllment of the requirements for the degree of Doctor of Philosophy in Engineering Mechanics Blacksburg, Virginia. 2003.
Haterbouch M., Benamar R. The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part I: iterative and explicit analytical solution for non-linear transverse vibration. Journal of Sound and Vibration. 265 – (123 – 154). 2003. https://doi.org/10.1016/S0022-460X(02)01443-8
Joshi S. J. Non-linear constitutive relations for piezoceramic materials. Smart Materials and Structures. Vol. 1, p. 80, 1992. https://doi.org/10.1088/0964-1726/1/1/012
Machado, S.P, Gatti, C.D., Ramirez, and Febbo, M., Influence of nonlinear constitutive relations in unimorphs piezoelectric harvesters. Journal of Physics: Conference Series, 773.012093, 2016. https://doi.org/10.1088/1742-6596/773/1/012093
Machado, S. Febbo, M. Dispositivos autónomos para el sensado inalámbrico de máquinas agrícolas. MECOM 2023, págs. 947-956. Concordia, Argentina. Noviembre 2023. ISSN 1666-6070
Mak K. H. Popov A. A, and McWilliam S. "Experimental model validation for a nonlinear energy harvester incorporating a bump stop" Journal of Sound and Vibration, vol. 331, pp. 2602-2623, 2012. https://doi.org/10.1016/j.jsv.2012.01.023
Reddy J. N. Theory and Analysis of Elastic Plates and Shells. (Boca Raton, FL: CRC Press), 2006.
Stanton S. C, Erturk A, Mann B. P, and Inman D. J. Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification. Journal of Applied Physics, vol. 108, p. 074903, 2010. https://doi.org/10.1063/1.3486519
Touzé C, Thomas O, and Chaigne A. Asymmetric non-linear forced vibrations of free-edge circular plates. Part 1: theory. Journal of Sound and Vibration, 258(4), 649–676. 2012. https://doi.org/10.1006/jsvi.2002.5143
Vera C, Febbo M, Machado S. Estudios paramétricos de un recolector de energía que utiliza piezoeléctricos de geometría circular. MECOM 2022, págs. 921-930 Bahía Blanca, Argentina, 2022. ISSN 1666-6070
Vera C, Febbo M, Machado S. Un modelo analítico para el estudio de recolectores de energía piezoeléctricos de geometría circular con condiciones de vinculación particulares. MECOM 2023, pags. 731 – 740 Concordia, Argentina, 2023. ISSN 1666-6070
Vera C, Machado S, Febbo M. Estudios analíticos y experimentales de recolectores de energía piezoeléctricos de geometría circular: análisis de la influencia de grandes aceleraciones para diferentes frecuencias. MECOM 2024, pags. 757 – 767. Rosario, Argentina, 2024. ISSN 1666-6070
Yang Y., Li Y., Guo Y., Xu B. -X and Yang T. Improved vibration-based energy harvesting by annular mass configuration of piezoelectric circular diaphragms. Smart Materials Structure. 27, 2018, 035004 (9pp), 2018. https://doi.org/10.1088/1361-665X/aaa586
Yuanlin Hu, Xin Liang and Wen Wang. A theorical solution of resonant circular diaphragmtype piezoactuators with added mass loads. Sensors an Actuators A: Physical. A 258 74- 87.2017. https://doi.org/10.1016/j.sna.2017.02.029
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