Stress in piezoelectric hollow sphere with thermal gradient

Abstract

The piezoelectric phenomenon has been exploited in science and engineering for decades. Recent advances in smart structures technology have led to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, we develop an analytic solution to the axisymmetric problem of a radially polarized, spherically isotropic piezoelectric hollow sphere. The sphere is subjected to uniform internal pressure, or uniform external pressure, or both and thermal gradient. There is a constant thermal difference between its inner and outer surfaces. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. Finally, the stress distributions in the sphere are obtained numerically for two piezoceramics.

The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators

“…For multilayered piezoelectric structures, a static analysis of electroelastic behaviors via the state space method has been presented by Chen et al [18]. Stress distribution in a homogeneous piezoelectric hollow sphere induced by a thermal gradient has been derived by Saadatfar and Rastgoo [19]. Analysis of the vibrational frequencies of a hollow piezoelectric sphere has been made by Heyliger and Wu [20].…”

Thermoelastic analysis of a rotating functionally graded cylindrical shell with functionally graded sensor and actuator layers on an elastic foundation placed in a constant magnetic field

“…Piezoelectric materials are one of the smart materials currently being used in structures to control deformation, vibration, buckling, and so on (Behjat et al, 2009;Bhattacharya et al, 1998;Brischetto and Carrera, 2009;Ghorbanpour Arani et al, 2006;Komijani et al, 2013;Saadatfar and Rastgoo, 2008;Saadatfar and Razavi, 2009). In recent years, smart structures including functionally graded materials (FGMs) or multilayered composite members bonded with piezoelectric actuators and sensors are extensively investigated.…”

Analytical solution of the thermoelasticity problem in a pressurized thick-walled sphere subjected to transient thermal loading

“…The analytical solution of the heat conduction equation and the Navier equation leads to the temperature profile, radial displacement, radial and hoop stresses as a function of the radial coordinate. Using Laplace transforms, an analytical solution for the transient heat conduction in spheres surrounded by a uniform temperature and finite Bi numbers also was obtained [6] Saadatfar and Rastgoo [7] developed an analytical solution to the problem of a radially polarized, spherically isotropic piezoelectric hollow sphere. They assumed there is a constant temperature difference between its inner and outer surfaces.…”