Stress Fields and Electric Potential in Piezoelectric Cylinders

چکیده مقاله

Piezoelectric materials produce an electric field by deformation and deform when subjected to an electric field. The coupling nature of piezoelectric materials has acquired wide applications in electro-mechanical and electric devices, including actuators, sensors, and structures. This paper explores a hollow circular cylinder composed of a radially polarized cylindrically anisotropic piezoelectric material, e.g., PZT_4 (a lead zirconium titanate) or BaTiO3 (barium titanate) under internal or external pressure and a constant potential difference between its inner and outer surfaces or a combination of these loadings. Electrodes attached to the inner and outer surfaces of the cylinder induce the potential difference. The governing equilibrium equations in polar form are shown to reduce to a coupled system of second-order ordinary differential equations for the radial displacement and electric potential field. These differential equations are analytically solved and, by considering seven different sets of boundary conditions, an analytic solution method is developed for boundary-value problems. The stress and electric potential distributions in the cylinder are discussed in detail for the two piezoceramics PZT_4 and BaTiO3.