Analytical Study of Piezoelectric Effect on Curvature and Mechanical Sensitivity in Large Deflection of Pre-Stressed Layered Plate Including a Piezoelectric Layer

Abstract:

This study explores the curvature and mechanical sensitivity of a pre-stressed layered plate embedded with a piezoelectric layer in large deflection. Piezoelectric effect was included in deriving the nonlinear governing equations but the arising nonlinear terms are neglected, yielding a standard Bessel equation or a modified Bessel equation for the lateral slope. Analytical solutions are developed and further manipulated to obtain lateral curvature and mechanical sensitivity. The results for a nearly monolithic plate under low pretension and low voltage applied across the piezoelectric layer agree well with those of CPT for a single-layered plate under pure mechanical loading. For typical symmetric 3-layered piezoelectric plates, the solutions show that, piezoelectric effect is apparent only up to a moderate initial tension. Beyond a moderate threshold value, the pretension turns to be dominant, resulting in nearly zero curvature and uniform mechanical sensitivity throughout the entire plate.

• Periodical: Applied Mechanics and Materials (Volume 775)
• Pages: 324-328
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.775.324
• Online since: July 2015
• Authors: Chun Fu Chen*, John Han Chen
• Keywords: Initial Tension, Large Deflection, Lateral Curvature, Mechanical Sensitivity, Piezoelectric Effect, Von Karman Plate Theory

References

[1] M. Shamshirsaz, M. Bahrami, M. B. Asgari, and M. Tayefeh, Analysis of Polysilicon Micro Beams Buckling with Temperature Dependent Properties, Proc. of DTIP (2007).

DOI: 10.1142/s1465876303001356

[2] C. H. J. Fox, X. Chen, and S. Mcsilliam, Analysis of the deflection of a circuar plate with an annular piezoelectric actuator, Sensors and Actuators A, 2007, 133, pp.180-194.

DOI: 10.1016/j.sna.2006.03.025

[3] J. A. Voorthuyzen, and P. Bergveld, The Influence of Tensile Forces on the Deflection Diaphragms in Pressure Sensors, Sensors Actuators A, 1984, 6, pp.201-213.

DOI: 10.1016/0250-6874(84)80021-9

[4] M. Sheplak, and J. Dugundji, Large Deflections of Clamped Circular Plates under Initial Tension and Transitions to Membrane Behavior, Trans. ASME, J. Appl. Mech., 1998, 65, pp.107-115.

DOI: 10.1115/1.2789012

[5] X. Zhang, K. -S. Chen, R. Ghodssi, A. Ayon, and S. M. Spearing, 2001, "Residual Stress and Fracture in Thick Tetraethylorthosilicate (TEOS) and Silane-based PECVD Oxide Films, Sensors and Actuators A, 91, p.373–380.

DOI: 10.1016/s0924-4247(01)00610-0

[6] P. M. Marcus, 1996, Curvature of Multilayer Epitaxial Films, J. Appl. Phys. 79, p.8364–8366.

[7] S. T. Cho, K. Najafi, and K. D. Wise, 1992, Internal Stress Compensation and Scaling in Ultra-sensitive Silicon Pressure Sensors, IEEE Transaction of Electron Devices, 39, pp.836-842.

DOI: 10.1109/16.127473

[8] D. -Y. Qiao, W. -Z. Yuan, Y. -T. Yu, Q. Liang, Z. -B. Ma, and X. -Y. Li, 2008, The Residual Stress-induced Buckling of Annular Thin Plates and Its Application in Residual Stress Measurement of Thin Films, Sensors and Actuators A, 143, p.409–414.

DOI: 10.1016/j.sna.2007.11.028

[9] R. Saini, S. Bhardwaj, T. Nishida, and M. Sheplak, 2000, Scaling Relations for Piezo-resistive Micro-phones, Proc. of IMECE 2000, p.1 – 8.

DOI: 10.1115/imece2000-1098

[10] S. Trolier-McKinstry and P. Muralt, 2004, Thin Film Piezoelectrics for MEMS, J. Electro-ceramics, 12, p.7–17.

DOI: 10.1023/b:jecr.0000033998.72845.51

[11] S. Kapuria and P. C. Dumir, 2005, Geometrically Nonlinear Axisymmetric Response of Thin Circular Plate under Piezoelectric Actuation, Communications in Nonlinear Science and Numerical Simulation, 10, p.411–423.

DOI: 10.1016/j.cnsns.2003.10.001

[12] C. -F. Chen, and J. -H. Chen, 2010, Analytical Geometrical Responses in Large Deflection of Simply Supported Piezo-electric Layered Plate under Initial Tension, Journal of the Chinese Institute of Engineers, 33, pp.1005-1013.

DOI: 10.1080/02533839.2010.9671689

[13] M. -X. Zhou, Q. -A. Huang, and M. Qin, 2005, Modeling, Design, and Fabrication of a Triple-Layered Capacitive Pressure Sensor, Sensors Actuators A, 117, pp.71-81.

DOI: 10.1016/j.sna.2004.05.036

[14] G. Wang, B. V. Sankar, L. N. Cattafesta, and M. Sheplak, 2002, Analysis of a Composite Piezoelectric Circular Plate with Initial Stress for MEMS, Proc. of 2002 ASME Int. Mech. Engng Congress & Exposition.

DOI: 10.1115/imece2002-39337