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Study on Electromechanical Behavior of Functionally Graded Piezoelectric Composite Beams

Published online by Cambridge University Press:  06 August 2020

Xiao Ma ,
Shuai Wang ,
Bo Zhou  and
Shifeng Xue
Xiao Ma
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China)Qingdao, China
Shuai Wang
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China)Qingdao, China
Bo Zhou*
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China)Qingdao, China
Shifeng Xue
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China)Qingdao, China
*
*Corresponding author (zhoubo@upc.edu.cn)
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Abstract

This paper investigates the electromechanical behavior of functionally graded piezoelectric composite beams containing axially functionally graded (AFG) beam and piezoelectric actuators subjected to electrical load. The mechanical properties of the AFG beam are assumed to be graded along the axial direction. Employing the electromechanical coupling theory and load simulation method, the expression for the simulation load of the piezoelectric actuators is obtained. Based on Euler-Bernoulli beam theory and the obtained simulation load, the differential governing equation of the piezoelectric composite beams subjected to electrical load is derived. The integration-by-parts approach is utilized to solve the differential governing equation, and the expression for the deflection of the piezoelectric composite beams is obtained. The accuracy of the proposed method is validated by the finite element method. The bending response of the functionally graded piezoelectric composite beams is investigated through the proposed method. In the numerical examples, the effects of electrical load, actuator thickness, AFG beam thickness and AFG beam length on the electromechanical behavior of the functionally graded piezoelectric composite beams are studied.

Keywords

Piezoelectric composite beamsaxially functionally gradedpiezoelectric actuatorselectromechanical behaviorintegration-by-parts approach
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 841 - 848
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

REFERENCES

Nikbakt, S., Kamarian, S. and Shakeri, M., “A review on optimization of composite structures part I: laminated composites,” Composite Structures, 195, pp.158-185 (2018).CrossRefGoogle Scholar
Ma, X. and Wei, G. F., “Numerical prediction of effective electro-elastic properties of three-dimensional braided piezoelectric ceramic composites,” Composite Structures, 180, pp.420-428 (2017).CrossRefGoogle Scholar
Pan, J., Bian, L., Gao, M., Liu, W. and Zhao, Y., “Reinforcement parameter effect on properties of three-phase composites,” Journal of Mechanics, 34, pp.629-636 (2018).CrossRefGoogle Scholar
Zenkour, A. M. and Sobhy, M., “Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates,” Journal of Mechanics, 28, pp.439-452 (2012).Google Scholar
Duc, N. D., Cong, P. H. and Quang, V. D., “Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment,” International Journal of Mechanical Sciences, 115, pp.711-722 (2016).CrossRefGoogle Scholar
Birman, V. and Byrd, L. W., “Modeling and analysis of functionally graded materials and structures,” Applied Mechanics Reviews, 60, pp.195-216 (2007).CrossRefGoogle Scholar
Huang, Y. and Li, X. F., “A new approach for free vibration of axially functionally graded beams with non-uniform cross-section,” Journal of Sound and Vibration, 329, pp.2291-2303 (2010).CrossRefGoogle Scholar
Shahba, A. and Rajasekaran, S., “Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials,” Applied Mathematical Modelling, 36, pp.3094-3111 (2012).CrossRefGoogle Scholar
Rajasekaran, S., “Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach,” Meccanica, 48, pp.1053-1070 (2013).CrossRefGoogle Scholar
Yuan, J. H., Pao, Y. H. and Chen, W. Q., “Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section,” Acta Mechanica, 227, pp.2625-2643 (2016).CrossRefGoogle Scholar
Fang, J. S. and Zhou, D., “Free vibration analysis of rotating axially functionally graded tapered Timoshenko beams,” International Journal of Structural Stability and Dynamics, 16, pp.1550007 (2016).CrossRefGoogle Scholar
Huang, Y. and Rong, H. W., “Free vibration of axially inhomogeneous beams that are made of functionally graded materials,” International Journal of Acoustics and Vibration, 22, pp.68-73 (2017).CrossRefGoogle Scholar
Ranjbar, M. and Feli, S., “Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam,” Polymer Composites, 39, pp.E969-E983 (2018).CrossRefGoogle Scholar
Xie, K., Wang, Y. W. and Fu, T. R., “Dynamic response of axially functionally graded beam with longitudinal-transverse coupling effect,” Aerospace Science and Technology, 85, pp.85-95 (2019).CrossRefGoogle Scholar
Cao, D. X. and Gao, Y. H., “Free vibration of nonuniform axially functionally graded beams using the asymptotic development method,” Applied Mathematics and Mechanics (English Edition), 40, pp.85-96 (2019).CrossRefGoogle Scholar
Mahmoud, M. A., “Natural frequency of axially functionally graded, tapered cantilever beams with tip masses,” Engineering Structures, 187, pp.34-42 (2019).CrossRefGoogle Scholar
Ma, X., Zhou, B. and Xue, S. F., “Investigation on actuation performance of continuous fiber reinforced piezoelectric composite actuator,” Journal of Mechanics, (2019).CrossRefGoogle Scholar
Arefi, M., Pourjamshidian, M. and Arani, A. G., “Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories,” European Physical Journal Plus, 133, pp.1-20 (2018).CrossRefGoogle Scholar
Bian, Z. G., Lim, C. W. and Chen, W. Q., “On functionally graded beams with integrated surface piezoelectric layers,” Composite Structures, 72, pp.339-351 (2006).CrossRefGoogle Scholar
Carbonari, R. C., Silva, E. C. N. and Paulino, G. H., “Topology optimization design of functionally graded bimorph-type piezoelectric actuators,” Smart Materials and Structures, 16, pp.2605-2620 (2007).CrossRefGoogle Scholar
Gharib, A., Salehi, M. and Fazeli, S., “Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators,” Materials Science and Engineering A, 498, pp.110-114 (2008).CrossRefGoogle Scholar
Fu, Y. M., Wang, J. Z. and Mao, Y. Q., “Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators,” Journal of Intelligent Material Systems and Structures, 22(18), pp.2093-2102 (2011).CrossRefGoogle Scholar
Jadhav, P. A. and Bajoria, K. M., “Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading,” Smart Materials and Structures, 21, pp.105005 (2012).CrossRefGoogle Scholar
Wu, C. P. and Chang, S. K., “Stability of carbon nanotube-reinforced composite plates with surface- bonded piezoelectric layers and under bi-axial compression,” Composite Structures, 111, pp.587-601 (2014).CrossRefGoogle Scholar
Shegokar, N. L. and Lal, A., “Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties,” Meccanica, 49, pp.1039-1068 (2014).CrossRefGoogle Scholar
Shen, H. S. and Yang, D. Q., “Nonlinear vibration of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators in thermal environments,” Engineering Structures, 90, pp.183-192 (2015).CrossRefGoogle Scholar
Lin, C. H. and Muliana, A., “Nonlinear electromechanical responses of functionally graded piezoelectric beams,” Composites Part B: Engineering, 72, pp.53-64 (2015).CrossRefGoogle Scholar
Bruant, I. and Proslier, L., “Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams,” International Journal of Mechanics and Materials in Design, 12, pp.173-192 (2016).CrossRefGoogle Scholar
Torki, M. E. and Reddy, J. N., “Buckling of functionally-graded beams with partially delaminated piezoelectric layers,” International Journal of Structural Stability and Dynamics, 16, pp.1450104 (2016).CrossRefGoogle Scholar
Zhang, L. W., Song, Z. G. and Liew, K. M., “Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches,” Composites Part B: Engineering, 85, pp.140-149 (2016).CrossRefGoogle Scholar
Kumar, R. S. and Ray, M. C., “Smart damping of geometrically nonlinear vibrations of functionally graded sandwich plates using 1-3 piezoelectric composites,” Mechanics of Advanced Materials and Structures, 23(6), pp.652-669 (2016).CrossRefGoogle Scholar
Zenkour, A. M. and Alghanmi, R. A., “Bending of exponentially graded plates integrated with piezoelectric fiber-reinforced composite actuators resting on elastic foundations,” European Journal of Mechanics A: Solids, 75, pp.461-471 (2019).CrossRefGoogle Scholar
Ghayesh, M. H., Farokhi, H., Gholipour, A. and Tavallaeinejad, M., “Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams,” International Journal of Engineering Science, 120, pp.51-62 (2017).CrossRefGoogle Scholar
Li, M., Chen, W. M., Wang, M. C. and Jia, L. J., “A load simulation method of piezoelectric actuator in FEM for smart structures,” Science in China Series E: Technological Sciences, 52(9), pp.2576-2584 (2009). (In Chinese)Google Scholar
Tang, J. G., “Computation of an infinite integral using integration by parts,” Mathematical Methods in the Applied Sciences, 41(3), pp.929-935 (2018).CrossRefGoogle Scholar