Static response of smart beams equipped with extension/shearing piezoelectric patches considering Poisson's effect based on different theories

Document Type : Research Article

Authors

1 Univesity of Tabriz

2 University of Tabriz

Abstract

This paper deals with the effect of Poisson's ratio on the static response of smart laminated composite beams. The actuation performance of smart beams with extension and shear mode piezoelectric orientation has been investigated. The first order and high order shear deformation beam theory has been implemented for modelling the problem. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. The state space approach is used to obtain an analytical solution for the response of smart beams with different boundary conditions. The effect of actuator length, location of piezoelectric patches, order of theory, fibre orientation, boundary condition and Poisson's ratio on the beam deflection, has been investigated. Also the response of beam with complete piezoelectric layer has been obtained with the same procedure and compared with the solution for the beams with piezoelectric patch of same length. Results show that neglecting Poisson's effect in calculations causes significant errors in the response of angle ply beam with extension mode actuators.

Highlights

[1] Aldraihem O. J.; Khdeir A. A., 2003. “Precise deflection analysnis of beams with piezoelectric patches.” Composite Structures: 60, 135-143.

[2] Zhang X. D.; Sun C. T., 1995. “Formulation of an adaptiv sandwich beam.” Smart Mater. Struct.: 4, 202-6.

[3] Benjeddou A.; Trindade M. A., 1999. Ohayon R.;“New Shear Actuated Smart Structure Beam Finite Element.” AIAA Journal: 37.

[4] Cheng Z. Q.; Lim C. W.; Kitipornchai S., 1999. “Threedimensional exact solution for inhomogeneous and laminated piezoelectric plates.” International Journal of Engineering Science: 37, 1425-1439.

[5] Aldraihem O. J.; Khdeir A. A., 2003. “Exact deflection solutions of beams with shear piezoelectric actuators.”International Journal of Solids and Structures: 40,1–12.

[6] Aldraihem O. J.; Khdeir A. A., 2006. ” Analytical solutions of antisymmetricangle-ply laminated plates with thickness–shear piezoelectric actuators.” Smart Mater. Struct.: 15, 232–242.

[7] Thinh T. I.; Ngoc L. K., 2010. “Static behavior and vibration control of piezoelectric cantilever composite plates and comparison with experiments.” Computational Materials Science: 49, S276–S280.

[8] Li X. Y.; Wu J.; Ding H. J.; Chen W. Q., 2011.“3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending.” International Journal of Engineering Science: 49, 664–676.

[9] Khdeir A. A.; Aldraihem O. J., 2011. “Exact analysis for static response of cross ply laminated smart shells.”Composite Structures: 94, 92–101.

[10] Behjat B.; Khoshravan M. R., 2012. “Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates.” Composite Structures: 94, 874–882.

[11] Khdeir A. A.; Aldraihem O. J., 2013. “Analytical investigation of laminated arches with extension and shear piezoelectric actuators.” European Journal of Mechanics A/Solids: 37, 185-192.

[12] Meirovitch L., 1967. “Analytical Methods In Vibrations” , Macmillan Publishing Co.

[13] Khdeir A. A.; Aldraihem O. J., 2001. “Deflection analysis of beams with extension and shear piezoelectric pathes using discontinuity functions.”Smart Mater. Struct.: 10, 212-220.

[14] Nazarzadeh Ansaroudi M.; Biglari H.; Jahangiri V.,2013. “Poisson and rotary inertia effects on natural frequency of composite beam based on high order theories”, 3rd conference on acoustics and vibration (ISAV2013), Tehran, Iran, December 25-26.

[15] Zhen W.; Wanji C., 2008. “An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams.” Composite Structures: 84, 337-349.

[16] Aldraihem O. J., Khdeir A. A, 2000. “Smart Beams with Extension and Thickness- Shear  iezoelectric Actuators” Smart Mater. Struct. 9 , 1- 9.

Keywords

Main Subjects

References

[1] Aldraihem O. J.; Khdeir A. A., 2003. “Precise deflection analysnis of beams with piezoelectric patches.” Composite Structures: 60, 135-143.
[2] Zhang X. D.; Sun C. T., 1995. “Formulation of an adaptiv sandwich beam.” Smart Mater. Struct.: 4, 202-6.
[3] Benjeddou A.; Trindade M. A., 1999. Ohayon R.;“New Shear Actuated Smart Structure Beam Finite Element.” AIAA Journal: 37.
[4] Cheng Z. Q.; Lim C. W.; Kitipornchai S., 1999. “Threedimensional exact solution for inhomogeneous and laminated piezoelectric plates.” International Journal of Engineering Science: 37, 1425-1439.
[5] Aldraihem O. J.; Khdeir A. A., 2003. “Exact deflection solutions of beams with shear piezoelectric actuators.”International Journal of Solids and Structures: 40,1–12.
[6] Aldraihem O. J.; Khdeir A. A., 2006. ” Analytical solutions of antisymmetricangle-ply laminated plates with thickness–shear piezoelectric actuators.” Smart Mater. Struct.: 15, 232–242.
[7] Thinh T. I.; Ngoc L. K., 2010. “Static behavior and vibration control of piezoelectric cantilever composite plates and comparison with experiments.” Computational Materials Science: 49, S276–S280.
[8] Li X. Y.; Wu J.; Ding H. J.; Chen W. Q., 2011.“3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending.” International Journal of Engineering Science: 49, 664–676.
[9] Khdeir A. A.; Aldraihem O. J., 2011. “Exact analysis for static response of cross ply laminated smart shells.”Composite Structures: 94, 92–101.
[10] Behjat B.; Khoshravan M. R., 2012. “Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates.” Composite Structures: 94, 874–882.
[11] Khdeir A. A.; Aldraihem O. J., 2013. “Analytical investigation of laminated arches with extension and shear piezoelectric actuators.” European Journal of Mechanics A/Solids: 37, 185-192.
[12] Meirovitch L., 1967. “Analytical Methods In Vibrations” , Macmillan Publishing Co.
[13] Khdeir A. A.; Aldraihem O. J., 2001. “Deflection analysis of beams with extension and shear piezoelectric pathes using discontinuity functions.”Smart Mater. Struct.: 10, 212-220.
[14] Nazarzadeh Ansaroudi M.; Biglari H.; Jahangiri V.,2013. “Poisson and rotary inertia effects on natural frequency of composite beam based on high order theories”, 3rd conference on acoustics and vibration (ISAV2013), Tehran, Iran, December 25-26.
[15] Zhen W.; Wanji C., 2008. “An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams.” Composite Structures: 84, 337-349.
[16] Aldraihem O. J., Khdeir A. A, 2000. “Smart Beams with Extension and Thickness- Shear  iezoelectric Actuators” Smart Mater. Struct. 9 , 1- 9.
Amirkabir Journal of Mechanical Engineering
Volume 48, Issue 4
January 2017
Pages 371-378

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