Advertisement

Journal of Elasticity

, Volume 38, Issue 2, pp 209–218 | Cite as

Saint-Venant's principle in linear piezoelectricity

  • R. C. Batra
  • J. S. Yang
Article

Abstract

Toupin's version of Saint-Venant's principle in linear elasticity is generalized to the case of linear piezoelectricity. That is, it is shown that, for a straight prismatic bar made of a linear piezoelectric material and loaded by a self-equilibrated system at one end only, the internal energy stored in the portion of the bar which is beyond a distance s from the loaded end decreases exponentially with the distance s.

Keywords

Internal Energy Piezoelectric Material Linear Elasticity Linear Piezoelectricity Linear Piezoelectric Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. E. Gurtin, The Linear Theory of Elasticity, Handbuch der Physik, Vol. VIa/2, ed. C. Truesdell, Springer-Verlag, Berlin, Heidelberg, New York (1972).Google Scholar
  2. 2.
    C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant's principle. Advances in Applied Mechanics, Vol. 23, edited by J. W. Hutchinson and T. Y Wu, Academic Press, New York (1983) pp. 179–269.Google Scholar
  3. 3.
    C. O. Horgan, Recent developments concerning Saint-Venant's principle: an update. Appl. Mech. Rev. (1989) 295–303.Google Scholar
  4. 4.
    R. A. Toupin, Saint-Venant's principle. Arch. Rat'l Mechanics Anal. 18 (1965) 83–96.Google Scholar
  5. 5.
    J. L. Ericksen, Uniformity in shells, Arch. Rat'l Mechanics Anal. 37 (1970) 73–84.Google Scholar
  6. 6.
    K. Berglund, Generalization of Saint-Venant's principle to micropolar continua. Arch Rat'l Mechanics Anal. 64 (1977) 317–326.Google Scholar
  7. 7.
    R. C. Batra, Saint-Venant's principle for a helical spring. Trans. ASME, J. Appl. Mechs. 45 (1978) 297–311.Google Scholar
  8. 8.
    R. C. Batra, Saint-Venant's principle for a micropolar helical body. Acta Mechanica 42 (1982) 99–109.Google Scholar
  9. 9.
    R. C. Batra, Saint-Venant's principle in linear elasticity with microstructure. Journal of Elasticity 13 (1983) 165–173.Google Scholar
  10. 10.
    H. F. Tiersten, Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969) pp. 33–39.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • R. C. Batra
    • 1
  • J. S. Yang
    • 2
  1. 1.Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of Mechanical Engineering, Aeronautical Engineering and MechanicsRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations