General Framework for Modeling Multifunctional Metamaterial Beam Based on a Derived One-Dimensional Piezoelectric Composite Finite Element
Publication: Journal of Aerospace Engineering
Volume 31, Issue 6
Abstract
Phononic crystals and metamaterials have been widely investigated over the last decade. In recent years, by integration with piezoelectric transducers, phononic/metamaterial-based piezoelectric energy harvesters (PEHs) have gained increasing research interest for achieving multifunctionalities. This paper proposes a general framework for modelling phononic/metamaterial beams bonded with piezoelectric transducers based on a one-dimensional piezoelectric composite finite element derived using the generalized Hamilton’s principle. A method for calculating band structures of infinitely long models of phononic/metamaterial beams that can carry piezoelectric transducers is then developed. This method is demonstrated via two case studies. The first case study investigates a metamaterial beam without piezoelectric coverage, and the proposed method is verified by the transfer matrix method (TMM). Compared with the TMM, the proposed method provides a dispersion relationship in a simpler form and thus demonstrates higher computational efficiency. The second case study investigates a metamaterial beam with periodic piezoelectric coverage. The proposed method takes into consideration the piezoelectric effect. Band structures of such a piezoelectric metamaterial beam under short-circuit and open-circuit conditions are evaluated. Subsequently, corresponding finitely long models of the two case studies are analyzed. The transmittances and open-circuit voltage responses of the piezoelectric transducers are then calculated. The predicted band gaps from transmittances match well with those from band structures. In addition, the transmittances and open-circuit voltage responses of piezoelectric transducers predicted based on the proposed model are verified against the finite-element solution produced by the ANSYS FE program.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is financially supported by the Energy Education Trust of New Zealand (No. 3708242) and the Ph.D. scholarship from China Scholarship Council (No. 201608250001).
References
Banerjee, A., R. Das, and E. P. Calius. 2017. “Frequency graded 1D metamaterials: A study on the attenuation bands.” J. Appl. Phys. 122 (7): 075101. https://doi.org/10.1063/1.4998446.
Carrara, M., M. R. Cacan, J. Toussaint, M. J. Leamy, M. Ruzzene, and A. Erturk. 2013. “Metamaterial-inspired structures and concepts for elastoacoustic wave energy harvesting.” Smart Mater. Struct. 22 (6): 065004. https://doi.org/10.1088/0964-1726/22/6/065004.
Chen, S., J. Wen, D. Yu, G. Wang, and X. Wen. 2011. “Band gap control of phononic beam with negative capacitance piezoelectric shunt.” Chin. Phys. B 20 (1): 014301. https://doi.org/10.1088/1674-1056/20/1/014301.
Chen, Z., B. Guo, Y. Yang, and C. Cheng. 2014. “Metamaterials-based enhanced energy harvesting: A review.” Phys. B Condens. Matter 438: 1–8. https://doi.org/10.1016/j.physb.2013.12.040.
Chen, Z., Y. Yang, Z. Lu, and Y. Luo. 2013. “Broadband characteristics of vibration energy harvesting using one-dimensional phononic piezoelectric cantilever beams.” Phys. B Condens. Matter 410: 5–12. https://doi.org/10.1016/j.physb.2012.10.029.
Erturk, A., and D. J. Inman. 2008. “A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters.” J. Vib. Acoust. 130 (4): 041002. https://doi.org/10.1115/1.2890402.
Hu, G., L. Tang, A. Banerjee, and R. Das. 2017a. “Meta-structure with piezoelectric element for simultaneous vibration suppression and energy harvesting.” J. Vib. Acoust. 139 (1): 011012. https://doi.org/10.1115/1.4034770.
Hu, G., L. Tang, and R. Das. 2017b. “Metamaterial-inspired piezoelectric system with dual functionalities: Energy harvesting and vibration suppression.” In Proc., SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring. Bellingham, Washington: International Society for Optics and Photonics.
Hu, G., L. Tang, R. Das, S. Gao, and H. Liu. 2017c. “Acoustic metamaterials with coupled local resonators for broadband vibration suppression.” AIP Adv. 7 (2): 025211. https://doi.org/10.1063/1.4977559.
Huang, H., C. Sun, and G. Huang. 2009. “On the negative effective mass density in acoustic metamaterials.” Int. J. Eng. Sci. 47 (4): 610–617. https://doi.org/10.1016/j.ijengsci.2008.12.007.
Junior, C. D. M., A. Erturk, and D. J. Inman. 2009. “An electromechanical finite element model for piezoelectric energy harvester plates.” J. Sound Vib. 327 (1): 9–25. https://doi.org/10.1016/j.jsv.2009.05.015.
Liu, Y., D. Yu, L. Li, H. Zhao, J. Wen, and X. Wen. 2007. “Design guidelines for flexural wave attenuation of slender beams with local resonators.” Phys. Lett. A 362 (5): 344–347. https://doi.org/10.1016/j.physleta.2006.10.056.
Lu, M., L. Feng, and Y. Chen. 2009. “Phononic crystals and acoustic metamaterials.” Mater. Today 12 (12): 34–42. https://doi.org/10.1016/S1369-7021(09)70315-3.
Mikoshiba, K., J. M. Manimala, and C. Sun. 2013. “Energy harvesting using an array of multifunctional resonators.” J. Intell. Mater. Syst. Struct. 24 (2): 168–179. https://doi.org/10.1177/1045389X12460335.
Page, J., A. Sukhovich, S. Yang, M. Cowan, F. Van Der Biest, A. Tourin, and P. Sheng. 2004. “Phononic crystals.” Phys. Status Solidi B 241 (15): 3454–3462. https://doi.org/10.1002/(ISSN)1521-3951.
Pai, P. F. 2010. “Metamaterial-based broadband elastic wave absorber.” J. Intell. Mater. Syst. Struct. 21 (5): 517–528. https://doi.org/10.1177/1045389X09359436.
Shen, L., J. Wu, S. Zhang, Z. Liu, and J. Li. 2015. “Low-frequency vibration energy harvesting using a locally resonant phononic crystal plate with spiral beams.” Mod. Phys. Lett. B 29 (1): 1450259. https://doi.org/10.1142/S0217984914502595.
Shu, Y., and I. Lien. 2006. “Analysis of power output for piezoelectric energy harvesting systems.” Smart Mater. Struct. 15 (6): 1499. https://doi.org/10.1088/0964-1726/15/6/001.
Sugino, C., V. Guillot, and A. Erturk. 2017a. “Multifunctional energy harvesting locally resonant metastructures.” In Proc., ASME 2017 Conf. on Smart Materials, Adaptive Structures and Intelligent Systems. New York: American Society of Mechanical Engineers.
Sugino, C., M. Ruzzene, and A. Erturk. 2017b. “Dynamics of hybrid mechanical-electromechanical locally resonant piezoelectric metastructures.” In Proc., ASME 2017 Conf. on Smart Materials, Adaptive Structures and Intelligent Systems. New York: American Society of Mechanical Engineers.
Sugino, C., Y. Xia, S. Leadenham, M. Ruzzene, and A. Erturk. 2017c. “A general theory for bandgap estimation in locally resonant metastructures.” J. Sound Vib. 406: 104–123. https://doi.org/10.1016/j.jsv.2017.06.004.
Tang, L., and Y. Yang. 2012. “A nonlinear piezoelectric energy harvester with magnetic oscillator.” Appl. Phys. Lett. 101 (9): 094102. https://doi.org/10.1063/1.4748794.
Xu, J., and J. Tang. 2017. “Modeling and analysis of piezoelectric cantilever-pendulum system for multi-directional energy harvesting.” J. Intell. Mater. Syst. Struct. 28 (3): 323–338. https://doi.org/10.1177/1045389X16642302.
Yang, Y., and L. Tang. 2009. “Equivalent circuit modeling of piezoelectric energy harvesters.” J. Intell. Mater. Syst. Struct. 20 (18): 2223–2235. https://doi.org/10.1177/1045389X09351757.
Yao, S., X. Zhou, and G. Hu. 2008. “Experimental study on negative effective mass in a 1D mass-spring system.” New J. Phys. 10 (4): 043020. https://doi.org/10.1088/1367-2630/10/4/043020.
Yu, D., Y. Liu, G. Wang, H. Zhao, and J. Qiu. 2006. “Flexural vibration band gaps in Timoshenko beams with locally resonant structures.” J. Appl. Phys. 100 (12): 124901. https://doi.org/10.1063/1.2400803.
Zhang, S. W., J. H. Wu, and Z. P. Hu. 2013. “Low-frequency locally resonant band-gaps in phononic crystal plates with periodic spiral resonators.” J. Appl. Phys. 113 (16): 163511. https://doi.org/10.1063/1.4803075.
Zhu, R., X. Liu, G. Hu, C. Sun, and G. Huang. 2014. “A chiral elastic metamaterial beam for broadband vibration suppression.” J. Sound Vib. 333 (10): 2759–2773. https://doi.org/10.1016/j.jsv.2014.01.009.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 31 • Issue 6 • November 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Feb 1, 2018
Accepted: Apr 23, 2018
Published online: Jul 17, 2018
Published in print: Nov 1, 2018
Discussion open until: Dec 17, 2018
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.