Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T10:57:31.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Analytical Study of Large Deflection of Piezoelectric Layered Plate Under Initial Tension

Published online by Cambridge University Press:  01 May 2013

C.-F. Chen  and
B.-C. Huang
C.-F. Chen*
Affiliation:
Department of Mechanical Engineering, Chung-Hua University, Hsin Chu, Taiwan 30067, R.O.C.
B.-C. Huang
Affiliation:
Department of Mechanical Engineering, Chung-Hua University, Hsin Chu, Taiwan 30067, R.O.C.
*
*Corresponding author ([email protected])
Get access

Abstract

The linear problem of large deflection of a clamped and layered piezoelectric circular plate under initial tension due to lateral pressure is solved. Von Karman plate theory for large deflection is extended to a symmetrically laminated case including a piezoelectric layer. The thus derived nonlinear governing equations are simplified by neglecting the arising nonlinear terms, yielding a modified Bessel equation or a standard Bessel equation for the lateral slope. These equations are solved analytically by imposing boundary conditions for the clamped edge. For a 3-layered nearly monolithic plate with a low applied voltage upon the piezoelectric layer, the results are in a good agreement with those available in literature for a single-layered plate under pure mechanical loading, thus validates the present approach. Typical 3-layered piezoelectric plates are then implemented and the results show that, piezoelectric effect seems to be apparent only up to a moderate initial tension. For a relatively high pretension, the effect of initial tension appears to be dominant, yielding nearly the same results for the structural responses, regardless of the piezoelectric effect, i.e., the magnitude of voltage applied upon the piezo-electric layer.

Keywords

Large deflectionPiezoelectric layered plateInitial tensionVon Karman plate theory
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 517 - 526
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Edition, McGraw-Hill, New York (1959).Google Scholar
2.Voorthuyzen, J. A. and Bergveld, P., “The Influence of Tensile Forces on the Deflection Diaphragms in Pressure Sensors,” Sensors and Actuators A, 6, pp. 201–213 (1984).Google Scholar
3.Sheplak, M. and Dugundji, J., “Large Deflections of Clamped Circular Plates under Initial Tension and Transitions to Membrane Behavior,” Journal of Applied Mechanics, ASME Transaction Journals, American Society of Mechanical Engineers, 65, pp. 107–115 (1998).Google Scholar
4.Su, Y. H., Chen, K. S., Roberts, D. C. and Spearing, S. M., “Large Deflection Analysis of a Pre-stressed Annular Plate with a Rigid Boss under Axisymmetric Loading,” Journal of Micromechanics and Microengineering, 11, pp. 645–653 (2001).Google Scholar
5.Cho, S. T., Najafi, K. and Wise, K. D., “Internal Stress Compensation and Scaling in Ultra-sensitive Silicon Pressure Sensors,” IEEE Transactions ED, ED39, pp. 836–842 (1992).Google Scholar
6.Chau, H.-L. and Wise, K. D., “Scaling Limits in Batch-fabricated Silicon Pressure Sensor,” IEEE Transactions ED, ED34, pp. 850–858 (1987).Google Scholar
7.Schellin, R., Strecker, M., Nothelfer, U. and Schuster, G., “Low Pressure Acoustic Sensors for Airborne Sound with Piezo-Resistive Mono-Crystalline Silicon and Electro-Chemically Etched Diaphragms,” Sensors and Actuators A, 46, pp. 156–160 (1995).CrossRefGoogle Scholar
8.Saini, R., Bhardwaj, S., Nishida, T. and Sheplak, M., “Scaling Relations for Piezo-resistive Micro-phones,” Proceedings of IMECE 2000, pp. 1–8 (2000).Google Scholar
9.Mukherjee, A. and Chaudhuri, A. S., “Piezolaminated Beams with Large Deflections,” International Journal of Solids and Structures, 39, pp. 4567–4582 (2002).Google Scholar
10.Mukherjee, A. and Chaudhuri, A. S., “Nonlinear Dynamic Response of Piezolaminated Smart Beams,” Computers and Structures, 83, pp. 1298–1304 (2005).Google Scholar
11.Pai, P. F., Nayfeh, A. H., Oh, K. and Mook, D. T., “A Refined Nonlinear Model of Piezoelectric Plate with Integrated Piezoelectric Sensors and Actuators,” International Journal of Solids and Structures, 30, pp. 1603–1630 (1993).Google Scholar
12.Liu, X., Wang, Q. and Quek, S. T., “Analytical Solution for Free Vibration of Piezoelectric Coupled Moderately Thick Circular Plates,” International Journal of Solids and Structures, 39, pp. 2129–2151 (2002).Google Scholar
13.Shen, H.-S., “Nonlinear Bending Analysis of Unsymmetric Cross-ply Laminated Plates with Piezoe-lectric Actuators in Thermal Environments,” Composite Structures, 63, pp. 167–177 (2004).Google Scholar
14.Varelis, D. and Saravanos, D. A., “Coupled Buckling and Postbuckling Analysis of Active Laminated Piezoelectric Composite Plates,” International Journal of Solids and Structures, 41, pp. 1519–1538 (2004).CrossRefGoogle Scholar
15.Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 9th Edition, Dover, New York, USA (1972).Google Scholar
16.Wang, G., Sankar, B. V., Cattafesta, L. N. and Sheplak, M., “Analysis of a Composite Piezoelectric Circular Plate with Initial Stress for MEMS,” Proceedings of 2002 ASME IMECE (Paper No.: 34337) (2002).Google Scholar