Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field

Abstract

The present paper deals with the analytical solution of a functionally graded piezoelectric (FGP) cylinder in the magnetic field under mechanical, thermal and electrical loads. All mechanical, thermal and electrical properties except Poisson ratio can be varied continuously and gradually along the thickness direction of the cylinder based on a power function. The cylinder is assumed to be axisymmetric. Steady state heat transfer equation is solved by considering the appropriate boundary conditions. Using Maxwell electro dynamic equation and assumed magnetic field along the axis of the cylinder, Lorentz's force due to magnetic field is evaluated for non homogenous state. This force can be employed as a body force in the equilibrium equation. Equilibrium and Maxwell equations are two fundamental equations for analysis of the problem. Comprehensive solution of Maxwell equation is considered in the present paper for general states of non homogeneity. Solution of governing equations may be obtained using solution of the characteristic equation of the system. Achieved results indicate that with increasing the non homogenous index, different mechanical and electrical components present different behaviors along the thickness direction. FGP can control the distribution of the mechanical and electrical components in various structures with good precision. For intelligent properties of functionally graded piezoelectric materials, these materials can be used as an actuator, sensor or a component of piezo motor in electromechanical systems. Piezoelectrics are new group of materials which can be used as a sensor or actuator in electromechanical systems. These materials can exchange the mechanical deformations into electric potential and conversely, the electric potential can be exchanged to mechanical deformation. Piezoelectric sensors or actuators may be designed as many structural elements such as beam, plate or cylindrical shell. Some applications of piezoelectric structures in sensor or actuator application, while the structure is subjected to magnetic field, is important for designer and engineer. Therefore it is necessary to analyze the functionally graded piezoelectric cylinders under magnetic field subjected to mechanical, thermal and electrical loads. Lim and He (2001) proposed an exact solution for a compositionally graded piezoelectric layer