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.
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References
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, England (1927).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow, Russia (1981).
W. Q. Chen, Problems of radially polarized piezoelastic bodies, International Journal of Solids and Structures 25 (1999) 3206–3221.
A. Ghorbanpour, S. Golabi, M. Saadatfar, Stress and Electric Potential Fields in Piezoelectric Smart spheres, Journal of Mechanical Science and Technology 20(11) (2006) 1920–1933.
D. K. Sinha, Note on the radial deformation of a piezoelectric, polarized spherical shell with a symmetrical distribution, J. Acoust. Soc. Am 34 (1962) 1073–1075.
D. Galic and C.O. Horgan, Internally Pressurized Radially Polarized Piezoelectric Cylinders, Journal of Elasticity 66 (2002) 257–272.
Y. Sugano, Transient thermal stresses in a transversely isotropic finite circular cylinder due to an arbitrary internal heat generation, Int. J. Eng. Sci. 17 (1979) 927–939.
G. A. Kardomateas, Transient thermal stresses in cylindrically orthotropic composite tubes, J. Appl. Mech. 56 (1989) 411–417.
G. A. Kardomateas, The initial phase of transient thermal stresses due to general boundary thermal loads in orthotropic hollow cylinders, J. Appl. Mech. 57 (1990) 719–724.
T. Hata, Thermal shock in a hollow sphere caused by rapid uniform heating, ASME J. Appl. Mech. 58 (1991) 64–69.
X. Wang, Thermal shock in a hollow cylinder caused by rapid arbitrary heating, J. Sound Vibrat. 183 (1995) 899–906.
X. Wang, The analytical solution of dynamic stress concentration in uniformly heated solid cylinder, J. Vibrat. Shock 15 (1996) 28–33.
A. M. Abd-Alla, Thermal stress in a transversely isotropic circular cylinder due to an instantaneous heat source, Appl. Math. Comput. 68 (1995) 113–124.
W. Q. Chen and T. Shioya, Piezothermoelastic behavior of a pyroelectric spherical shell, J. Thermal Stress 24 (2001) 105–120.
J. Q. Tarn, Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads, Int. J. Solids Structure 38 (2001) 8189–8206.
P. F. Hou, H. M. Wang and H. J. Ding, Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder, Int. J. Eng. Sci. 41 (2003) 1849–1868.
H. L. Dai and X. Wang, Stress wave propagation in laminated piezoelectric spherical shells under thermal shock and electric excitation, European Journal of Mechanics A/Solids 24 (2005) 263–276.
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Saadatfar, M., Rastgoo, A. Stress in piezoelectric hollow sphere with thermal gradient. J Mech Sci Technol 22, 1460–1467 (2008). https://doi.org/10.1007/s12206-008-0423-8
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DOI: https://doi.org/10.1007/s12206-008-0423-8