Electrothermomechanical behavior of a radially polarized rotating functionally graded piezoelectric cylinder

Abstract

A hollow circular cylinder made of exponentially graded piezoelectric material, such as PZT_4, is considered. Loading is composed of internal and external pressures, a distributed temperature field due to steady state heat conduction with convective boundary condition, an inertia body force due to rotation with constant angular velocity and a constant electric potential difference between its inner and outer surfaces. The material properties except Poisson's ratio and thermal conduction coefficient are assumed to be exponentially distributed along radius. The governing equation in polarized form is shown to reduce to a second-order ordinary differential equation with variable coefficients for the radial displacement. In this article, a closed form solution is presented for this ODE by employing hypergeometric functions such as Whittaker's M and W functions. Also we have considered four different sets of boundary conditions. The electrothermomechanical induced stresses and the electric potential distributions are investigated for the piezoceramic PZT_4 cylinder. It is concluded that the inhomogeneity exponent µ plays a substantial role in radial and circumferential stress distributions. Therefore, the results of this investigation can contribute to the design of EGPM rotating thick-walled circular cylinders.A list of symbols can be found on page 881.

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

“…Similar idea of using power function material properties can be found in numerous articles [9][10][11][12][13][14][15][16][17][18]. A few groups proposed different assumptions that [19][20][21] the material parameters were assumed as exponential function. For instance, the elastic stiffness was ij ij 0 ( ) In the above papers, material parameters (the elastic stiffness, piezoelectric coefficient and the dielectric constant) of FGPM cylinder are assumed to be power functions or exponential functions, which imply FGPM cylinder comprises of multi-layers.…”

“…Furthermore, the distinction between the hoop stress and radial stress is discussed to decrease the pressure concentration in FGPM cylinder. x new variables about r F Hypergeometric function α, β, δ constants in hypergeometric function f i (i=1, 2, K., 6) coefficients in equation (19) P(r), Q(r) two linearly independent solutions of equation (22) G(r) a particular solution of equation (…”

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

“…The FGM and FGPM layers properties are assumed to change along the thickness direction z as follows [18][19] :…”

Electro-elastic analysis of functionally graded piezoelectric variable thickness cylindrical shells using a first-order electric potential theory and perturbation technique

“…The 1D exact solution of this problem was obtained on the assumption of long cylinder while properties of material changes in the thickness direction as well as stress distribution were studied. Ghorbanpour et al (2011), like Arefi and Rahimi (2012), conducted stress analysis in a cylinder with an exponential function expression for material non-homogeneity. The analysis of active control in vibrations for conical shells was carried out by Li et al (2012) using piezoelectric materials.…”