Saint-Venant's principle in linear piezoelectricity
- 155 Downloads
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.
KeywordsInternal Energy Piezoelectric Material Linear Elasticity Linear Piezoelectricity Linear Piezoelectric Material
Unable to display preview. Download preview PDF.
- 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.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.C. O. Horgan, Recent developments concerning Saint-Venant's principle: an update. Appl. Mech. Rev. (1989) 295–303.Google Scholar
- 4.R. A. Toupin, Saint-Venant's principle. Arch. Rat'l Mechanics Anal. 18 (1965) 83–96.Google Scholar
- 5.J. L. Ericksen, Uniformity in shells, Arch. Rat'l Mechanics Anal. 37 (1970) 73–84.Google Scholar
- 6.K. Berglund, Generalization of Saint-Venant's principle to micropolar continua. Arch Rat'l Mechanics Anal. 64 (1977) 317–326.Google Scholar
- 7.R. C. Batra, Saint-Venant's principle for a helical spring. Trans. ASME, J. Appl. Mechs. 45 (1978) 297–311.Google Scholar
- 8.R. C. Batra, Saint-Venant's principle for a micropolar helical body. Acta Mechanica 42 (1982) 99–109.Google Scholar
- 9.R. C. Batra, Saint-Venant's principle in linear elasticity with microstructure. Journal of Elasticity 13 (1983) 165–173.Google Scholar
- 10.H. F. Tiersten, Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969) pp. 33–39.Google Scholar