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A Second-Order Solution of Saint-Venant's Problem for a Piezoelectric Circular Bar Using Signorini's Perturbation Method

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Abstract

We study electromechanical deformations of a homogeneous transversely isotropic piezoelectric prismatic circular bar loaded only at the end faces. The constitutive relations for the material of the bar are taken to be quadratic in the displacement gradients and the electric field. It is found that the two end faces of the bar when twisted with no electric charge applied to them will exhibit a difference in the electric potential. Thus the piezoelectric cylinder could be used to measure the torque or the angular twist.

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References

  1. J.H. Poynting, On pressure perpendicular to the shear-planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc. Roy. Soc. London, A82(1909) 546-549.

    ADS  Google Scholar 

  2. C.A. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics, Handbuch der Physik (S. Flügge, ed.), Vol. III/3, Springer-Verlag, Berlin (1965).

    Google Scholar 

  3. C.-C. Wang and C.A. Truesdell, Introduction to Rational Elasticity, Noordhoff Int. Publishing, Leyden (1973).

    MATH  Google Scholar 

  4. A. Signorini, Sulle deformazioni termoelastiche finite. Proc. 3rd Int. Congr. Appl. Mechs. 2(1930) 80-89.

    Google Scholar 

  5. A.E. Green and J.E. Adkins, Large Elastic Deformations and Nonlinear Continuum Mechanics, Claredon Press, Oxford (1960).

    Google Scholar 

  6. R.S. Rivlin, The solution of problems in second order elasticity theory. J. Rational Mechs. Analysis 2(1953) 53-81.

    MathSciNet  Google Scholar 

  7. A.E. Green and R.T. Shield, Finite extension and torsion of cylinder. Proc. Roy. Soc. London 244(1951) 47-86.

    MATH  MathSciNet  ADS  Google Scholar 

  8. F. dell'Isola, G.C. Ruta and R.C. Batra, A second-order solution of Saint-Venant's problem for an elastic pretwisted bar using Signorini's Perturbation Method. J. Elasticity 49(1998) 113-127.

    Article  MATH  MathSciNet  Google Scholar 

  9. A.-J.-C. B. Saint-Venant, Mémoire sur la torsion des prismes. Meéoires des Savants étrangers 14(1856) 233.

    Google Scholar 

  10. F. dell'Isola, G.C. Ruta and R.C. Batra, Generalized Poynting effects in predeformed-prismatic bars, J. Elasticity 50(1998) 181-196.

    Article  MATH  Google Scholar 

  11. A.C. Eringen and G.A. Maugin, Electrodynamics of Continua, Springer-Verlag, New York (1989).

    Google Scholar 

  12. J.S. Yang and R.C. Batra, A second-order theory of piezoelectric materials. J. Acoustic Soc. America 97(1995) 280-288.

    Article  ADS  Google Scholar 

  13. R.C. Batra and J.S. Yang, Saint-Venant's principle in linear piezoelectricity, J. Elasticity 38(1995) 209-218.

    Article  MATH  MathSciNet  Google Scholar 

  14. R.A. Toupin, Saint-Venant's principle, Arch. Rat'l Mechanics Anal. 18(1965) 83-96.

    MATH  MathSciNet  ADS  Google Scholar 

  15. D. Iesan, Saint-Venant's problem for inhomogeneous and anisotropic elastic bodies. J. Elasticity 6(1976) 277-294.

    Article  MATH  Google Scholar 

  16. D. Iesan, On Saint-Venant's problem for elastic dielectrics, J. Elasticity 21(1989) 101.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Iesan, Saint-Venant's Problem, Springer-Verlag, New York, NY (1987).

    MATH  Google Scholar 

  18. D. Iesan and L. Nappa, Saint-Venant's problem for microstretch elastic solids. Int. J. Engng. Sci. 32(1994) 229-236.

    Article  MATH  MathSciNet  Google Scholar 

  19. F. dell'Isola and L. Rosa, Saint-Venant problem in linear piezoelectricity in Mathematics and Control in Smart Structures, V.V. Varadhan, ed., SPIE, Vol. 2715, 399-409, Feb. 1996.

  20. F. dell'Isola and L. Rosa, Almansi-type boundary conditions for electric potential inducing flexure in linear piezoelectric beams. Cont. Mechs. & Thermodynamics 9(1997) 115-125.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. F. Daví, Saint Venant's problem for linear piezoelectric bodies. J. Elasticity 43(1996) 227-245.

    Article  MATH  MathSciNet  Google Scholar 

  22. F. dell'Isola and R.C. Batra, Saint-Venant's problem for porous linear elastic materials. J. Elasticity 47(1997) 73-81.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, MC 0219, Blacksburg, VA, 24061, U.S.A.

    R.C. Batra

  2. Dipartimento di Ingegneria Strutturale e Geotecnica, Universitá di Roma “La Sapienza”, 00184, Roma, Italy

    F. dell'Isola & S. Vidoli

Authors
  1. R.C. Batra
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  2. F. dell'Isola
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  3. S. Vidoli
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Batra, R., dell'Isola, F. & Vidoli, S. A Second-Order Solution of Saint-Venant's Problem for a Piezoelectric Circular Bar Using Signorini's Perturbation Method. Journal of Elasticity 52, 75–90 (1998). https://doi.org/10.1023/A:1007534931590

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  • DOI: https://doi.org/10.1023/A:1007534931590

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