Effect of Electric Potential Distribution on Electromechanical Behavior of a Piezoelectrically Sandwiched Micro-Beam

Document Type: Research Paper

Authors

Mechanical Engineering Department, Urmia University

Abstract

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is derived according to Euler-Bernoulli beam theory and considering the voltage applied to the  piezoelectric layers and Maxwell’s equations for the two dimensional electric potential distribution. The obtained nonlinear equation solved by step by step linearization method and Galerkin weighted residual method. The effects of the electric potential distribution and the ratio of the piezoelectric layer thickness respect to the elastic layer thickness on the mechanical behavior of the micro-beam are investigated. The obtained results are compared with the results of a model in which electric potential distribution is not considered.

Keywords

[1] Fathalilou M., Motallebi A., Yagubizade H., Rezazadeh G., Shirazi K., Alizadeh Y., 2009, Mechanical Behavior of an Electrostatically-Actuated Micro-beam under Mechanical Shock, Journal of Solid Mechanics 1: 45-57.

[2] Yao J.J., 2000, RF-MEMS from a device perspective, Journal of Micromechanics and Micro engineering 10: 9-38.

[3] Afrang S., Abbaspour E., 2002, A low voltage electrostatic torsional micro machined microwave actuator, In: Proceedings of the 2002 IEEE international conference on semiconductor electronics (ICSE 2002) Penang, Malaysia 100–104.

[4] Balaraman D., Bhattacharya S.K., 2002, Low-cost low actuation voltage copper RF MEMS actuators. In: Proceeding of the Microwave Symposium Digest, 2002 IEEE MTT-S International, Seattle, WA 2: 1225–1228.

[5] Peroulis D., Pacheo S.P., Sarabandi K., 2003, Electromechanical considerations in developing low-voltage RF MEMS actuators, IEEE Transaction on microwave theory and thecniques 51(1): 259–270.

[6] Sbaizero O., Lucchini E., 1996, Influence of residual stresses on the mechanical properties of a layered ceramic composite, Journal of the European Ceramic Society 16(8): 813-818.

[7] Pascual J., Lube T., Danzer R., 2008, Fracture statistics of ceramic laminates strengthened by compressive residual stresses, Journal of the European Ceramic Society 28(8): 1551-1556.

[8] Hayes M., Rivlin R.S., 1961, Surface waves in deformed elastic materials, Archive for Rational Mechanics and Analysis 8: 359–439.

[9] Hirao M., Fukuoka H., Hori K., 1981, Acoustoelastic effect of Rayleigh surface wave in isotropic material, Journal of Applied Mechanics 48: 119–43.
[10] Kumar A., Weizel U., Mittemeijer E.J., 2006, Analysis of gradients of mechanical stresses by X-ray diffraction measurements at fixed penetration/information depths, Journal of Applied Crystallography39: 633-646.

[11] Cammarata R.C., Sieradzki, K., Spaepen, F., 2000, Simple model for interface stresses with application to misfit dislocation generation in epitaxial thin films, Journal of Applied Physics 87(3): 1227-1234.

[12] Freund L.B., Suresh S., 2003, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press.

[13] Quang H.L., He Q.C., 2009, Estimation of the effective thermo-elastic moduli of fibrous nano composites with cylindrically anisotropic phases, Archive for Applied Mechanics 79: 225–248.

[14] Hosseinzadeh A., Ahmadian M.T., 2010, Application of Piezoelectric and Functionally Graded Materials in Designing Electrostatically Actuated Micro Switches, Journal of Solid Mechanics 2: 179-189.

[15] Coughlin M.F., Stamenovic D., Smits J.G., 1996, Determining material stiffness using piezoelectric bimorphs, in: Proceedings of the 1996 IEEE ultrasonic Symposium 2: 1607–1610.

[16] Mortet V., Petersen R., Haenen K., Olieslaeger M. D., 2006, Wide range pressure sensor based on a piezoelectric bimorph micro-cantilever, Applied Physic Letters 88 (13) : 133511–15.

[17] Olli K., Kruusing A., Pudas M., Rahkonen T., 2009, Piezoelectric bimorph charge mode force sensor. Journal of Sensors and Actuators A: Physical 153: 42–49.

[18] Rezazadeh G., Tahmasebi A., Zubstov M., 2006, Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage, Microsystem Technologies 12: 1163–1170.

[19] Zamanian M., Khadem S.E., Mahmoodi S.N., 2008 , The effect of a piezoelectric layer on the mechanical behavior of an electrostatic actuated micro-beam, Smart Materials and Structures 17 : 065024–15.

[20] Rezazadeh G., Tahmasebi A., 2009, Electromechanical behavior of micro-beams with piezoelectric and electrostatic actuation, Sensing and Imaging: an International Journal 10: 15–30.

[21] Rezazadeh G., Fathalilou M., Shabani R., 2009, Static and dynamic stabilities of a microbeam actuated by a piezoelectric voltage, Microsystem Technologies 15: 1785–1791.

[22] Azizi S., Rezazadeh G., Ghazavi M.R., Esmaeilzadeh Khadem S.,2012, Parametric excitation of a piezoelectrically actuated system near Hopf bifurcation, Journal of Applied Mathematical Modelling 36 : 1529–1549.

[23] Quek S.T., Wang Q., 2000, On dispersion relations in piezoelectric coupled plate Structures, Smart Material Structure 9: 859–67.

[24] Moheimani R., Fleming A.J., 2006, Piezoelectric Transducers for Vibration Control and Damping (Advances in Industrial Control), First Edition, Springer.

[25] Zhu M., Leighton G., 2008, Dimensional Reduction Study of Piezoelectric Ceramics Constitutive Equations from 3-D to 2-D and 1-D, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55(11): 2377-2383.

[26] Pietrzakowski M., 2007, Piezoelectric control of composite plate vibration: Effect of electric potential distribution, Computers and Structures 86: 948–954.

[27] Kant T., Shiyekar S.M., 2008, Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory, Computers and Structures 86 : 1594–1603.

[28] Nabian A., Rezazadeh G., Haddad-derafshi M., Tahmasebi A., 2008, Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and non-uniform electrostatic pressure, Microsystem Technologies 14: 235–240.

[29] Nayfeh A.H., Mook D.T., 1979, Nonlinear oscillations. Wiley, NewYork, Microsystem Technologies 14: 235–240.

[30] Ramamurty U., Sridhar S., Giannakopolos A. E., Suresh S., 1999, An experimental study of spherical indentation on piezoelectric materials, Acta material 47(8): 2417-2430.

[31] Crawley E. F., Luis J. D., 1987, Use of piezoelectric actuators as elements of intelligent structures, AIAA Journal 25(10): 1373–1385.