Stress and Electric Potential Fields in Piezoelectric Smart Spheres

  • Ghorbanpour, A. (Department of Mechanical Engineering University of Kashan) ;
  • Golabi, S. (Department of Mechanical Engineering University of Kashan) ;
  • Saadatfar, M. (Department of Mechanical Engineering University of Kashan)
  • Published : 2006.11.01

Abstract

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 electric-mechanical and electric devices, including electric-mechanical actuators, sensors and structures. In this paper, a hollow sphere composed of a radially polarized spherically anisotropic piezoelectric material, e.g., PZT_5 or (Pb) (CoW) $TiO_3$ under internal or external uniform pressure and a constant potential difference between its inner and outer surfaces or combination of these loadings has been studied. Electrodes attached to the inner and outer surfaces of the sphere induce the potential difference. The governing equilibrium equations in radially polarized 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 solved analytically for seven different sets of boundary conditions. The stress and the electric potential distributions in the sphere are discussed in detail for two piezoceramics, namely PZT _5 and (Pb) (CoW) $TiO_3$. It is shown that the hoop stresses in hollow sphere composed of these materials can be made virtually uniform across the thickness of the sphere by applying an appropriate set of boundary conditions.

Keywords

References

  1. Berlincourt, D. A., 1971, 'Piezoelectric Crystals and Ceramics,' In: O. E. Mattiat (ed.), Ultrasonic Transducer Materials, Plenum Press, New York 63-124
  2. Chen, W. Q. and Shioya, T., 2001. 'Piezothermoelastic Behavior of a Pyroelectric Spherical Shell,' J. Thermall Stress, 24, pp. 105-120 https://doi.org/10.1080/01495730150500424
  3. Chen, W. Q., 1998, 'Problems of Radially Polarized Piezoelastic Bodies,' International Journal of Solids and Structures 36, pp.4317-4332 https://doi.org/10.1016/S0020-7683(98)00204-2
  4. Destuynder, P., 1999, 'A Few Remarks on the Controllability of an Aeroacoustic Model Using Piezo-Devices,' In: J. Holnicki-Szulc and J. Rodellar (eds), Smart Structures. Kluwer Academic Publishers, Dordrecht pp. 53-62
  5. Fung, Y. C. 1965. Foundations of Solid Mechanics, Prentice-Hall, New York
  6. Heyliger, P. and Wu, Y. -C., 1999. 'Electroelastic Fields in Layered Piezoelectric Spheres,' International Journal of Engineering Science 37, pp. 143-161 https://doi.org/10.1016/S0020-7225(98)00068-8
  7. Jiang, H. W., Schmid, F., Brand, W. and Tomlinson, G. R., 1999, 'Controlling Pantograph Dynamics Using Smart Technology,' In: J. Holnicki-Szulc and J. Rodellar (eds), Smart Kluwer structures. Academic Publishers, Dordrecht pp. 125-132
  8. Kawiecki, G., 1999, 'Piezogenerated Elastic Waves for Structural Health Monitoring,' In: J. Holnicki-Szulc and J. Rodellar (eds), Smart Structures, Kluwer Academic Publishers, Dordrecht pp. 133-142
  9. Lekhnitskii, S. G., 1981, Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow
  10. Love, A. E. H., 1927, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge
  11. Sinha, D. K., 1962. 'Note on the Radial Deformation of a Piezoelectric, Polarized Spherical shell with a Symmetrical Distribution,' J. Acoust. Soc. Am. 34, pp. 1073-1075 https://doi.org/10.1121/1.1918247
  12. Tiersten, H. F., 1969. Linear Piezoelectric Plate Vibrations, Plenum Press, New York