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The influence of Murnaghan constants on the propagation of a torsional wave in pre-stretched compound circular cylinders

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The propagation of torsional waves in prestressed compound circular cylinders is investigated modeling them by a piecewise-homogeneous body and using the three-dimensional linearized theory of elastic waves in prestressed body. It is assumed that the elastic relations for the components of the cylinders include the Murnaghan potential. The numerical investigations are performed for bronze (Br) or brass (Pr) (for the solid cylinder) and steel (St) (for the hollow cylinder). The effect of the variation of the geometric (the ratio of the thickness of the outer cylinder to the radius of the inner cylinder) and mechanical parameters on the dispersion curves are analyzed using the numerical results obtained

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References

  1. S. D. Akbarov, “The influence of the third order elastic constants on the dynamical interface stress field in a half-space covered with a pre-stretched layer,” Int. J. Non-Linear Mech., 41, 417–425 (2006).

    Article  ADS  Google Scholar 

  2. S. D. Akbarov, “Dynamical (time-harmonic) axisymmetric interface stress field in the finite pre-strained half-space covered with the finite pre-stretched layer,” Int. J. Eng. Sci., 44, 93–112 (2006).

    Article  MathSciNet  Google Scholar 

  3. S. D. Akbarov, “On the dynamical axisymmetric stress field in the finite pre-stretched bilayered slab resting on the rigid foundation,” J. Sound Vibr., 294, 221–237 (2006).

    Article  ADS  Google Scholar 

  4. S. D. Akbarov, “Frequency response of the axisymmetrically finite pre-stretched slab from incompressible functionally graded material on a rigid foundation,” Int. J. Eng. Sci., 44, 484–500 (2006).

    Article  MathSciNet  Google Scholar 

  5. S. D. Akbarov, “Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review),” Int. Appl. Mech., 43, No. 12, 1305–1324 (2007).

    Article  Google Scholar 

  6. S. D. Akbarov and A. N. Guz, “Axisymmetric longitudinal wave propagation in pre-stressed compound circular cylinders,” Int. J. Eng. Sci., 42, 769–791 (2004).

    Article  Google Scholar 

  7. S. D. Akbarov, I. Emiroglu, and F. Tasci, “The Lamb’s problem for a half-space covered with the pre-stretched layer,” Int. J. Mech. Sci., 47, 1326–1349 (2005).

    Article  MATH  Google Scholar 

  8. S. D. Akbarov and M. Ozisik, “The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane,” Int. J. Eng. Sci., 41, 2047–2061 (2003).

    Article  Google Scholar 

  9. S. D. Akbarov and M. Ozisik, “Dynamic interaction of a prestressed nonlinear elastic layer and a half-plane,” Int. App. Mech., 40, No. 9, 1056–1063 (2004).

    Article  Google Scholar 

  10. A. E. Armenakas, “Torsinal waves in composite rods,” J. Acoust. Soc. Am., 38, 439–446 (1965).

    Article  ADS  Google Scholar 

  11. J. R. Berger, P. A. Martin, and S. J. McCaffery, “Time-harmonic torsional wave in a composite cylinder with an imperfect interface,” J. Acoust. Soc. Am., 107, 1161–1167 (2000).

    Article  ADS  Google Scholar 

  12. H. Demiray and E. S. Suhubi, “Small torsional oscillations of an initially twisted circular rubber cylinder,” Int. J. Eng. Sci., 8, 19–30 (1970).

    Article  MATH  Google Scholar 

  13. A. C. Eringen and E. S. Suhubi, Elastodynamics, Vol. 1, Academic Press (1975).

  14. A. E. Green, “Torsional vibrations of an initially stressed circular cylinder,” in: Problems of Continuum Mechanics, Muskhelishvili Anniversary Vol., Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania (1961), pp. 148–154.

  15. A. E. Green, “A note on wave propagation in initially deformed bodies,” J. Mech. Phys. Solids, 11, No. 2, 119–126 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  16. A. N. Guz, General Theory, Vol. 1 of the two-volumes series Elastic Waves in Prestressed Bodies [in Russian], Naukova Dumka, Kyiv (1986).

  17. A. N. Guz, Propagation Laws, Vol. 2 of the two-volumes series Elastic Waves in Prestressed Bodies [in Russian], Naukova Dumka, Kyiv (1986).

  18. A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A. S. K., Kyiv (2004).

  19. A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).

    Article  MathSciNet  Google Scholar 

  20. A. N. Guz, “Three-dimensional theory of stability of a carbon nanotube in matrix,” Int. Appl. Mech., 41, No. 1, 19–31 (2006).

    Article  Google Scholar 

  21. A. N. Guz and I. A. Guz, “On models in the theory of multiwalled carbon nanotubes in matrix,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).

    Article  MathSciNet  Google Scholar 

  22. A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondestructive stress analysis of solids,” Int. Appl. Mech., 36, No. 9, 1119–1149 (2000).

    Article  Google Scholar 

  23. A. N. Guz, J. J. Rushchitsky, and I. A. Guz, “Establishing fundamentals of the mechanics of nanocomposites,” Int. Appl. Mech., 43, No. 3, 247–271 (2007).

    Article  Google Scholar 

  24. D. W. Haines and P. C. Y. Lee, “Axially symmetric torsional waves in circular composite cylinders,” J. Appl. Mech., 38, 1042–1044 (1971).

    Article  Google Scholar 

  25. D. W. Haines and P. C. Y. Lee, “Approximate theory of torsional wave propagation in elastic circular composite cylinders,” J. Acoust. Soc. Am., 49, No. 1, 211–219 (1971).

    Article  MATH  ADS  Google Scholar 

  26. M. Hayes and R. S. Rivlin, “Surface waves in deformed materials,” Archive for Rational Mech. Anal., 8, No. 5, 358–380 (1961).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  27. R. K. Kaul, R. P. Shaw, and W. Muller, “Torsional waves in an axially homogeneous bimetallic cylinder,” Int. J. Solids Struct., 17, 379–394 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  28. J. Kudlicka, “Dispersion of torsional waves in thick-walled transversely isotopic circular cylinder of infinite length,” J. Sound and Vib., 294, 368–373 (2006).

    Article  ADS  Google Scholar 

  29. F. D. Murnaghan, Finite Deformation of an Elastic Solid, J. Wiley and Sons, New York (1951).

    MATH  Google Scholar 

  30. R. Parnes, “Torsional dispersion relation of waves in an infinitely long clad cylindrical rod,” J. Acoust. Soc. Am., 71, No. 6, 1347–1351 (1982).

    Article  MATH  ADS  Google Scholar 

  31. R. C. Reuter, “First-branch dispersion of torsional waves in bimaterial rods,” J. Acoust. Soc. Am., 46, 821–823 (1969).

    Article  ADS  Google Scholar 

  32. E. S. Suhubi, “Small longitudinal vibration of an initially stretched circular cylinder,” Int. J. Eng. Sci., 2, 509–517 (1965).

    Article  MathSciNet  Google Scholar 

  33. R. N. Thurston, “Torsional acoustic modes in clad rods,” IEEE Trans. on Sonics and Ultrasonics, SU-23, No. 3, 154–161 (1976).

    Google Scholar 

  34. Ya. A. Zhuk and I. A. Guz, “Influence of prestress on the velocities of waves propagating normally to the layers of nanocomposites,” Int. Appl. Mech., 42, No. 7, 729–743 (2006).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Besiktas, Istanbul, Turkey, 34349

    S. D. Akbarov

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan, 370141

    S. D. Akbarov

  3. Department of Physics, Gebze Institute of Technology, Gebze, Kocaeli, Turkey, 41400

    A. Ozturk

Authors
  1. S. D. Akbarov
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  2. A. Ozturk
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Correspondence to S. D. Akbarov.

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Published in Prikladnaya Mekhanika, Vol. 46, No. 7, pp. 134–144, July 2010.

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Akbarov, S.D., Ozturk, A. The influence of Murnaghan constants on the propagation of a torsional wave in pre-stretched compound circular cylinders. Int Appl Mech 46, 847–856 (2010). https://doi.org/10.1007/s10778-010-0374-5

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