Static Deflection of Hinged-Hinged piezoelectric Multilayer Beam Under Different Loading Conditions

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

افشین منوچهری‌فر ¹ , علیرضا جلیلی ²

1 - استادیار دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر
2 - دانشجوی کارشناسی ارشد مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر

Received: 2015-10-03 Accepted : 2015-10-03 Published : 2008-09-22

Keywords: Piezoelectric, Multilayer beam, Constituent equations, Bimorph, Unimorph,

Abstract :

In this paper at first introduced constituent equations for piezoelectric and then by the help of this equations, internal energy of hinged-hinged piezoelectric multilayer beam was computed. Then by the principle of minimum potential energy and Rayleigh -Ritz method the bending curvature equation of hinged-hinged piezoelectric multilayer beam under concentrated moment, concentrated force, uniform pressure load and applied electrical voltage with satisfaction of boundary conditions are guessed. Unknown coefficients are determined by the principle of minimum potential energy. Thereinafter obtained equations have simplified for hinged-hinged unimorph and bimorph beam. Electrical load and voltage produced in unimorph and bimorph beam as sensor are calculated. In order to verify the derived equations for a hinged-hinged piezoelectric multilayer bending beam, the analytical calculation compared with ANSYS 10 results by some finite element examples.

References:

[1] Reza Moheimani S.O., Fleming A.J., Piezoelectric transducers for vibration control and damping. - (Advances in industrial control), Springer-Verlag London Limited, UK, 2006.

[2] Gordan T.L., Ounaies Z., Piezoelectric Ceramics Characterization, ICASE Report,  NO.28, 2001.

[3] Park J.K., Moon W.K., Constitutive Relations for Piezoelectric Benders Under Various Boundary Conditions, Journal Sensors and Actuator A: Physical, volume 117, 2005, pp. 159-167.

[4] Smits J.G., Choi W., The Constituent Equations of Piezoelectric Heterogeneous Bimorphs, IEEE Transactions on Ultrasonic, Ferroelectrics, and Frequency Control, Volume 38, No.3, 1991.

[5] Yocum M., Abramovich H., Static Behavior of Piezoelectric Actuated Beams, Computers & Structures, Volume 80, Number 23, 2002, pp. 1797-1808

[6] Fernandes A., Pouget J., Analytical and numerical approaches to piezoelectric bimorph, International Journal of Solid and Structures, Volume 40, 2003, pp. 4331- 4352.

[7] Balls R.G., Schlaak H.F., Schmid A.J., The Constituent Equations of Piezoelectric Multilayer Bending Actuators in Closed Analytical Form and Experimental Results, Journal Sensors &Actuators .A: Physical, 2006, pp. 1-7.

[8] Yang J., An Introduction to The Theory of Piezoelectricity, Department of Engineering Mechanics University of Nebraska-Lincoln, U.S.A. , 2005.