Simulation of Piezoelectric Laminated Smart Structure under Strong Electric Field
Applying strong electric field on piezoelectric actuators,
on one hand very significant electroelastic material nonlinear effects
will occur, on the other hand piezo plates and shells may undergo
large displacements and rotations. In order to give a precise
prediction of piezolaminated smart structures under large electric
field, this paper develops a finite element (FE) model accounting for
both electroelastic material nonlinearity and geometric nonlinearity
with large rotations based on the first order shear deformation
(FSOD) hypothesis. The proposed FE model is applied to analyze
a piezolaminated semicircular shell structure.
[1] J. S. Moita, P. G. Martins, C. M. M. Soares, and C. A. M. Soares,
“Optimal dynamic control of laminated adaptive structures using a
higher order model and a genetic algorithm,” Computers and Structures,
vol. 86, pp. 198–206, 2008.
[2] S.-Q. Zhang, R. Schmidt, P. C. M¨uller, and X.-S. Qin, “Disturbance
rejection control for vibration suppression of smart beams and plates
under a high frequency excitation,” Journal of Sound and Vibration,
vol. 353, pp. 19–37, 2015.
[3] D. F. Nelson, “Theory of nonlinear electroacoustics of dielectric,
piezoelectric, and pyroelectric crystals,” The Journal of the Acoustical
Society of America, vol. 63, no. 6, pp. 1738–1748, 1978.
[4] H. F. Tiersten, “Electroelastic interactions and the piezoelectric
equations,” The Journal of the Acoustical Society of America, vol. 70,
no. 6, pp. 1567–1576, 1981.
[5] S. Li, W. Cao, and L. E. Cross, “The extrinsic nature of nonlinear
behavior observed in lead zirconate titanate ferroelectric ceramic,”
Journal of Applied Physics, vol. 69, no. 10, pp. 7219–7224, 1991.
[6] A. J. Masys, W. Ren, G. Yang, and B. K. Mukherjee, “Piezoelectric
strain in lead zirconate titante ceramics as a function of electric field,
frequency, and dc bias,” Journal of Applied Physics, vol. 94, no. 2, pp.
1155–1162, 2003.
[7] C. M. Landis, “Non-linear constitutive modeling of ferroelectrics,”
Current Opinion in Solid State and Materials Science, vol. 8, pp. 59–69,
2004.
[8] L. Ma, Y. Shen, J. Li, H. Zheng, and T. Zou, “Modeling hysteresis
for piezoelectric actuators,” Journal of Intelligent Material Systems and
Structures, vol. 27, no. 10, pp. 1404–1411, 2016.
[9] Q.-M. Wang, Q. Zhang, B. Xu, R. Liu, and L. E. Cross, “Nonlinear
piezoelectric behavior of ceramic bending mode actuators under strong
electric fields,” Journal of Applied Physics, vol. 86, no. 6, pp.
3352–3360, 1999.
[10] L. Q. Yao, J. G. Zhang, L. Lu, and M. O. Lai, “Nonlinear dynamic
characteristics of piezoelectric bending actuators under strong applied
electric,” Journal of Microelectromechanical Systems, vol. 13, no. 4, pp.
645–652, 2004.
[11] Z. K. Kusculuoglu and T. J. Royston, “Nonlinear modeling of composite
plates with piezoceramic layers using finite element analysis,” Journal
of Sound and Vibration, vol. 315, pp. 911–926, 2008. [12] S. Panda and M. C. Ray, “Nonlinear finite element analysis of
functionally graded plates integrated with patches of piezoelectric fiber
reinforced composite,” Finite Elements in Analysis and Design, vol. 44,
pp. 493–504, 2008.
[13] R. Schmidt and T. D. Vu, “Nonlinear dynamic FE simulation of smart
piezolaminated structures based on first- and third-order transverse shear
deformation theory,” Advanced Materials Research, vol. 79 - 82, pp.
1313–1316, 2009.
[14] S. Lentzen, P. Klosowski, and R. Schmidt, “Geometrically nonlinear
finite element simulation of smart piezolaminated plates and shells,”
Smart Materials and Structures, vol. 16, pp. 2265–2274, 2007.
[15] S. Q. Zhang and R. Schmidt, “Large rotation FE transient analysis
of piezolaminated thin-walled smart structures,” Smart Materials and
Structures, vol. 22, p. 105025, 2013.
[16] S. Zhang and R. Schmidt, “Static and dynamic FE analysis of
piezoelectric integrated thin-walled composite structures with large
rotations,” Composite Structures, vol. 112, pp. 345–357, 2014.
[17] L. Q. Yao, J. G. Zhang, L. Lu, and M. O. Lai, “Nonlinear extension
and bending of piezoelectric laminated plate under large applied field
actuation,” Smart Materials and Structures, vol. 13, pp. 404–414, 2004.
[18] L. M. Habip, “Theory of elastic shells in the reference state,”
Ingenieur-Archiv, vol. 34, pp. 228–237, 1965.
[19] L. Librescu, Elastostatics and Kinetics of Anisotropic and
Heterogeneous Shell-Type Structures. Leyden: Noordhoff International,
1975.
[20] I. Kreja and R. Schmidt, “Large rotations in first-order shear deformation
FE analysis of laminated shells,” International Journal of Non-Linear
Mechanics, vol. 41, pp. 101–123, 2006.
[21] CTS Corporation: http://www.ctscorp.com/ (accessed on 17/02/1017).
[22] S. Kapuria and M. Y. Yasin, “A nonlinear efficient layerwise finite
element model for smart piezolaminated composites under strong
applied electric field,” Smart Materials and Structures, vol. 22, p.
055021, 2013.
[1] J. S. Moita, P. G. Martins, C. M. M. Soares, and C. A. M. Soares,
“Optimal dynamic control of laminated adaptive structures using a
higher order model and a genetic algorithm,” Computers and Structures,
vol. 86, pp. 198–206, 2008.
[2] S.-Q. Zhang, R. Schmidt, P. C. M¨uller, and X.-S. Qin, “Disturbance
rejection control for vibration suppression of smart beams and plates
under a high frequency excitation,” Journal of Sound and Vibration,
vol. 353, pp. 19–37, 2015.
[3] D. F. Nelson, “Theory of nonlinear electroacoustics of dielectric,
piezoelectric, and pyroelectric crystals,” The Journal of the Acoustical
Society of America, vol. 63, no. 6, pp. 1738–1748, 1978.
[4] H. F. Tiersten, “Electroelastic interactions and the piezoelectric
equations,” The Journal of the Acoustical Society of America, vol. 70,
no. 6, pp. 1567–1576, 1981.
[5] S. Li, W. Cao, and L. E. Cross, “The extrinsic nature of nonlinear
behavior observed in lead zirconate titanate ferroelectric ceramic,”
Journal of Applied Physics, vol. 69, no. 10, pp. 7219–7224, 1991.
[6] A. J. Masys, W. Ren, G. Yang, and B. K. Mukherjee, “Piezoelectric
strain in lead zirconate titante ceramics as a function of electric field,
frequency, and dc bias,” Journal of Applied Physics, vol. 94, no. 2, pp.
1155–1162, 2003.
[7] C. M. Landis, “Non-linear constitutive modeling of ferroelectrics,”
Current Opinion in Solid State and Materials Science, vol. 8, pp. 59–69,
2004.
[8] L. Ma, Y. Shen, J. Li, H. Zheng, and T. Zou, “Modeling hysteresis
for piezoelectric actuators,” Journal of Intelligent Material Systems and
Structures, vol. 27, no. 10, pp. 1404–1411, 2016.
[9] Q.-M. Wang, Q. Zhang, B. Xu, R. Liu, and L. E. Cross, “Nonlinear
piezoelectric behavior of ceramic bending mode actuators under strong
electric fields,” Journal of Applied Physics, vol. 86, no. 6, pp.
3352–3360, 1999.
[10] L. Q. Yao, J. G. Zhang, L. Lu, and M. O. Lai, “Nonlinear dynamic
characteristics of piezoelectric bending actuators under strong applied
electric,” Journal of Microelectromechanical Systems, vol. 13, no. 4, pp.
645–652, 2004.
[11] Z. K. Kusculuoglu and T. J. Royston, “Nonlinear modeling of composite
plates with piezoceramic layers using finite element analysis,” Journal
of Sound and Vibration, vol. 315, pp. 911–926, 2008. [12] S. Panda and M. C. Ray, “Nonlinear finite element analysis of
functionally graded plates integrated with patches of piezoelectric fiber
reinforced composite,” Finite Elements in Analysis and Design, vol. 44,
pp. 493–504, 2008.
[13] R. Schmidt and T. D. Vu, “Nonlinear dynamic FE simulation of smart
piezolaminated structures based on first- and third-order transverse shear
deformation theory,” Advanced Materials Research, vol. 79 - 82, pp.
1313–1316, 2009.
[14] S. Lentzen, P. Klosowski, and R. Schmidt, “Geometrically nonlinear
finite element simulation of smart piezolaminated plates and shells,”
Smart Materials and Structures, vol. 16, pp. 2265–2274, 2007.
[15] S. Q. Zhang and R. Schmidt, “Large rotation FE transient analysis
of piezolaminated thin-walled smart structures,” Smart Materials and
Structures, vol. 22, p. 105025, 2013.
[16] S. Zhang and R. Schmidt, “Static and dynamic FE analysis of
piezoelectric integrated thin-walled composite structures with large
rotations,” Composite Structures, vol. 112, pp. 345–357, 2014.
[17] L. Q. Yao, J. G. Zhang, L. Lu, and M. O. Lai, “Nonlinear extension
and bending of piezoelectric laminated plate under large applied field
actuation,” Smart Materials and Structures, vol. 13, pp. 404–414, 2004.
[18] L. M. Habip, “Theory of elastic shells in the reference state,”
Ingenieur-Archiv, vol. 34, pp. 228–237, 1965.
[19] L. Librescu, Elastostatics and Kinetics of Anisotropic and
Heterogeneous Shell-Type Structures. Leyden: Noordhoff International,
1975.
[20] I. Kreja and R. Schmidt, “Large rotations in first-order shear deformation
FE analysis of laminated shells,” International Journal of Non-Linear
Mechanics, vol. 41, pp. 101–123, 2006.
[21] CTS Corporation: http://www.ctscorp.com/ (accessed on 17/02/1017).
[22] S. Kapuria and M. Y. Yasin, “A nonlinear efficient layerwise finite
element model for smart piezolaminated composites under strong
applied electric field,” Smart Materials and Structures, vol. 22, p.
055021, 2013.
@article{"International Journal of Architectural, Civil and Construction Sciences:76328", author = "Shun-Qi Zhang and Shu-Yang Zhang and Min Chen", title = "Simulation of Piezoelectric Laminated Smart Structure under Strong Electric Field", abstract = "Applying strong electric field on piezoelectric actuators,
on one hand very significant electroelastic material nonlinear effects
will occur, on the other hand piezo plates and shells may undergo
large displacements and rotations. In order to give a precise
prediction of piezolaminated smart structures under large electric
field, this paper develops a finite element (FE) model accounting for
both electroelastic material nonlinearity and geometric nonlinearity
with large rotations based on the first order shear deformation
(FSOD) hypothesis. The proposed FE model is applied to analyze
a piezolaminated semicircular shell structure.", keywords = "Smart structures, piezolamintes, material nonlinearity,
geometric nonlinearity, strong electric field.", volume = "11", number = "9", pages = "1270-4", }
