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

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 AN SYS 10 results by some finite element examples.