A Comprehensive Study on Nonlinear Functionally Graded Piezoelectric Harvesters under Moving Loads
Publication: Journal of Engineering Mechanics
Volume 146, Issue 5
Abstract
The goal in this research was to investigate harvesting energy from a nonlinear functionally graded beam with bonded piezoelectric patch under multiple moving loads. The material of the harvester was considered to be varied in the thickness direction. The generalized Hamilton’s principle and von Kármán nonlinear theory were used to obtain a coupled system of differential equations considering nonlinear geometry as well as electromechanical coupling. The Newmark time integration scheme as well as the finite-element method were used to obtain the numerical results. Numerical study was also performed to investigate the effects of velocity of the moving loads, time lags between the moving loads, beam length, material distribution, and piezoelectric patch location on the harvested power. Results indicate that the aforementioned parameters have significant effects on the harvested power. The results show that ignoring the nonlinear effects especially for considerable values of moving loads results in erroneous large values for the harvested power. To the best of authors’ knowledge, there is no other study about energy harvesting from nonlinear vibrations of beams under moving loads.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some data and models are available from the corresponding author by request (including data of this research and MATLAB figures).
References
Amini, Y., P. Fatehi, M. Heshmati, and H. Parandvar. 2016. “Time domain and frequency domain analysis of functionally graded piezoelectric harvesters subjected to random vibration: Finite element modeling.” Compos. Struct. 136 (Feb): 384–393. https://doi.org/10.1016/j.compstruct.2015.10.029.
Amini, Y., M. Heshmati, P. Fatehi, and S. E. Habibi. 2017a. “Energy harvesting from vibrations of a functionally graded beam due to moving loads and moving masses.” J. Eng. Mech. 143 (9): 04017063. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001272.
Amini, Y., M. Heshmati, P. Fatehi, and S. E. Habibi. 2017b. “Piezoelectric energy harvesting from vibrations of a beam subjected to multi-moving loads.” Appl. Math. Modell. 49 (Sep): 1–16. https://doi.org/10.1016/j.apm.2017.04.043.
Chen, Y. 1999. “Distribution of vehicular loads on bridge girders by the FEA using ADINA: Modeling, simulation, and comparison.” Comput. Struct. 72 (1–3): 127–139. https://doi.org/10.1016/S0045-7949(99)00032-2.
Crandall, S. H. 1968. Dynamics of mechanical and electromechanical systems. New York: McGraw-Hill.
Fatehi, P., and M. Farid. 2018. “Piezoelectric energy harvesting from nonlinear vibrations of functionally graded beams: Finite-element approach.” J. Eng. Mech. 145 (1): 04018116. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001547.
Heshmati, M., and Y. Amini. 2019. “A comprehensive study on the functionally graded piezoelectric energy harvesting from vibrations of a graded beam under travelling multi-oscillators.” Appl. Math. Modell. 66 (Feb): 344–361. https://doi.org/10.1016/j.apm.2018.09.002.
Khalili, S., A. Jafari, and S. Eftekhari. 2010. “A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads.” Compos. Struct. 92 (10): 2497–2511. https://doi.org/10.1016/j.compstruct.2010.02.012.
Malekzadeh, P., and S. Monajjemzadeh. 2016. “Dynamic response of functionally graded beams in a thermal environment under a moving load.” Mech. Adv. Mater. Struct. 23 (3): 248–258. https://doi.org/10.1080/15376494.2014.949930.
Malekzadeh, P., and A. Shojaee. 2014. “Dynamic response of functionally graded beams under moving heat source.” J. Vib. Control 20 (6): 803–814. https://doi.org/10.1177/1077546312464990.
Pesterev, A. V., B. Yang, L. A. Bergman, and C. A. Tan. 2001. “Response of elastic continuum carrying multiple moving oscillators.” J. Eng. Mech. 127 (3): 260–265. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:3(260).
Priya, S., D. Popa, and F. Lewis. 2006. “Energy efficient mobile wireless sensor networks.” In Proc., ASME 2006 Int. Mechanical Engineering Congress and Exposition, 491–498. New York: ASME.
Reddy, J. N. 2014. An introduction to nonlinear finite element analysis: With applications to heat transfer, fluid mechanics, and solid mechanics. Oxford, UK: Oxford University Press.
Roundy, S., P. K. Wright, and J. Rabaey. 2003. “A study of low level vibrations as a power source for wireless sensor nodes.” Comput. Commun. 26 (11): 1131–1144. https://doi.org/10.1016/S0140-3664(02)00248-7.
Sheng, G., and X. Wang. 2017. “The geometrically nonlinear dynamic responses of simply supported beams under moving loads.” Appl. Math. Modell. 48 (Aug): 183–195. https://doi.org/10.1016/j.apm.2017.03.064.
Şimşek, M. 2010. “Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load.” Compos. Struct. 92 (10): 2532–2546. https://doi.org/10.1016/j.compstruct.2010.02.008.
Şimşek, M., and T. Kocatürk. 2009. “Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load.” Compos. Struct. 90 (4): 465–473. https://doi.org/10.1016/j.compstruct.2009.04.024.
Şimşek, M., T. Kocatürk, and Ş. Akbaş. 2012. “Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load.” Compos. Struct. 94 (8): 2358–2364. https://doi.org/10.1016/j.compstruct.2012.03.020.
Sladek, J., V. Sladek, P. L. Bishay, and F. Garcia-Sanchez. 2015. “Influence of electric conductivity on intensity factors for cracks in functionally graded piezoelectric semiconductors.” Int. J. Solids Struct. 59 (May): 79–89. https://doi.org/10.1016/j.ijsolstr.2015.01.012.
Wu, C., M. Kahn, and W. Moy. 1996. “Piezoelectric ceramics with functional gradients: A new application in material design.” J. Am. Ceram. Soc. 79 (3): 809–812. https://doi.org/10.1111/j.1151-2916.1996.tb07951.x.
Xiang, H. J., J. J. Wang, Z. F. Shi, and Z. W. Zhang. 2013. “Theoretical analysis of piezoelectric energy harvesting from traffic induced deformation of pavements.” Smart Mater. Struct. 22 (9): 095024. https://doi.org/10.1088/0964-1726/22/9/095024.
Yan, T., S. Kitipornchai, J. Yang, and X. Q. He. 2011. “Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load.” Compos. Struct. 93 (11): 2992–3001. https://doi.org/10.1016/j.compstruct.2011.05.003.
Yang, J., Y. Chen, Y. Xiang, and X. L. Jia. 2008. “Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load.” J. Sound Vib. 312 (1–2): 166–181. https://doi.org/10.1016/j.jsv.2007.10.034.
Younesian, D., M. H. Kargarnovin, D. J. Thompson, and C. J. C. Jones. 2006. “Parametrically excited vibration of a timoshenko beam on random viscoelastic foundation jected to a harmonic moving load.” Nonlinear Dyn. 45 (1–2): 75–93. https://doi.org/10.1007/s11071-006-1460-4.
Zhu, S., D. Zhang, K. C. Zhou, and X. F. Li. 2015. “Effects of nonhomogeneity on singular electroelastic field near electrodes for a functionally graded piezoelectric material.” Eur. J. Mech. A. Solids 51 (May): 21–28. https://doi.org/10.1016/j.euromechsol.2014.11.009.
Zhu, X., and Z. Meng. 1995. “Operational principle, fabrication and displacement characteristics of a functionally gradient piezoelectric ceramic actuator.” Sens. Actuators, A 48 (3): 169–176. https://doi.org/10.1016/0924-4247(95)00996-5.
Information & Authors
Information
Published In
Copyright
©2020 American Society of Civil Engineers.
History
Received: May 25, 2019
Accepted: Nov 6, 2019
Published online: Feb 20, 2020
Published in print: May 1, 2020
Discussion open until: Jul 20, 2020
Authors
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.