Acta Mechanica Solida Sinica

, Volume 24, Issue 6, pp 527–538 | Cite as

Wave Propagation in a Transversely Isotropic Thermoelastic Solid Cylinder of Arbitrary Cross-Section

Article

Abstract

The wave propagation in an infinite, homogeneous, transversely isotropic solid cylinder of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.

Key words

vibration of thermal cylinder thermoelastic stress three-dimensional stress analysis wave propagation in an arbitrary cross-section 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Nagaya, K., Dispersion of elastic waves in bar with arbitrary cross-section. Journal of Acoustical society of America, 1981, 70(3): 763–770.CrossRefGoogle Scholar
  2. [2]
    Nagaya, K., Direct method on determination of eigen frequencies of arbitrary shaped plates. Transaction of the ASME, Journal of vibration, Stress and Reliability in Design, 1983, 105: 132–136.CrossRefGoogle Scholar
  3. [3]
    Mirsky, I., Wave propagation in a transversely isotropic circular cylinders. Part I: Theory; Part II: Numerical results. Journal of Acoustical Society of America, 1964, 37(6): 1016–1026.CrossRefGoogle Scholar
  4. [4]
    Chau, K.T., Vibration of transversely isotropic finite circular cylinders. Transaction of the ASME, Journal of Applied Mechanics, 1994, 61: 964–970.CrossRefGoogle Scholar
  5. [5]
    Honarvar, F. and Sinclair, A.N., Acoustic wave scattering from transversely isotropic cylinders. Journal of Acoustical Society of America, 1996, 100: 57–63.CrossRefGoogle Scholar
  6. [6]
    Honarvar, F., Enjilela, E., Sinclair, A.N. and Mirnezami, S.A., Wave propagation in a transversely isotropic cylinders. International Journal of Solid and Structure, 2007, 44: 5236–5246.CrossRefGoogle Scholar
  7. [7]
    Pan, Y., Rossignol, C. and Audoin, B., Acoustic waves generated by a laser point source in an isotropic cylinder. Journal of Acoustical society of America, 2004, 116(2): 814–820.CrossRefGoogle Scholar
  8. [8]
    Biot, M.A., Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 1956, 27(3): 240–253.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Suhubi, E.S., Longitudinal vibrations of a circular cylindrical coupled with a thermal field. Journal of Mechanical Physics Solids, 1964, 12: 69–75.CrossRefGoogle Scholar
  10. [10]
    Erbay, S. and Suhubi, E.S., Longitudinal wave propagation in a generalized thermoelastic cylinder. Journal of Thermal Stresses, 1986, 9: 279–295.CrossRefGoogle Scholar
  11. [11]
    Green, A.E. and Naghdi, P.M., Thermoelasticity without energy dissipation. Journal of Elasticity, 1993, 31: 189–208.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Kumar, A.B., Thermoelastic waves from suddenly punched hole in stretched elastic plate. Indian Journal of Pure and Applied Mathematics, 1989, 20(2): 181–188.MATHGoogle Scholar
  13. [13]
    Sharma, J.N. and Sharma, P.K., Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel. Journal of Thermal Stresses, 2002, 25: 169–182.CrossRefGoogle Scholar
  14. [14]
    Singh, H. and Sharma, J.N., Generalized thermoelastic waves in transversely isotropic media. Journal of Acoustical society of America, 1985, 77(3): 1046–1053.CrossRefGoogle Scholar
  15. [15]
    Kardomateas, G.A., Transient thermal stresses in cylindrically orthotropic composite tubes. Journal of Applied Mechanics, 1989, 56: 411–417.CrossRefGoogle Scholar
  16. [16]
    Yee, K.C. and Moon, T.J., Plane thermal stress analysis of an orthotropic cylinder subjected to an arbitrary, transient, asymmetric temperature distribution. Transaction of the ASME, Journal of Applied Mechanics, 2002, 69: 632–640.CrossRefGoogle Scholar
  17. [17]
    Venkatesan, M. and Ponnusamy, P., Wave propagation in a solid cylinder of arbitrary cross-section immersed in a fluid. Journal of Acoustical society of America, 2002, 112: 936–942.CrossRefGoogle Scholar
  18. [18]
    Venkatesan, M. and Ponnusamy, P., Wave propagation in a solid cylinder of polygonal cross-section immersed in a fluid. Indian Journal of Pure and Applied Mathematics, 2003, 34(9): 1381–1391.MATHGoogle Scholar
  19. [19]
    Chen, W.Q., Ying, J. and Yang, Q.D., Free vibrations of transversely isotropic cylinders and cylindrical shells. Transaction of the ASME, Journal of Pressure Vessel Technology, 1998a, 120(4), 321–324.CrossRefGoogle Scholar
  20. [20]
    Chen, W.Q., Ding, H. and Xu, R., On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells. International Journal of Pressure Vessels and piping, 1998b, 75(13): 961–996.CrossRefGoogle Scholar
  21. [21]
    Chen, W.Q., Lim, C.W. and Ding, H.J., Point temperature solution for a penny-shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium. Engineering Analysis with Boundary Elements, 2005, 29: 524–532.CrossRefGoogle Scholar
  22. [22]
    Lin-xiang, W. and Melnik, R.V.N., Differential-algebraic approach to coupled problems of dynamic thermoelasticity. Applied Mathematics and Mechanics, 2006, 27(9): 1185–1196.CrossRefGoogle Scholar
  23. [23]
    Youssef, H.M. and El-Bary, A.A., Mathematical model for thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity. Journal of Computational Methods in Science and Technology, 2006, 12(2): 165–171.CrossRefGoogle Scholar
  24. [24]
    Youssef, H.M. and Abbas, I.A., Thermal shock problem of a generalized thermoelasticity of an infinitely long annular cylinder with variable thermal conductivity. Journal of Computational Methods in Science and Technology, 2007, 13(2): 95–100.CrossRefGoogle Scholar
  25. [25]
    Berliner, M.J. and Solecki, R., Wave propagation in fluid-loaded transversely isotropic cylinders. Part 1 analytical formulation, Part II, numerical results. Journal of Acoustical society of America, 1996, 99: 1841–1853.CrossRefGoogle Scholar
  26. [26]
    Antia, H.M., Numerical Methods for Scientists and Engineers. Hindustan Book Agency, New Delhi, 2000.MATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.Department of MathematicsGovt. Arts College (Autonomous)CoimbatoreIndia

Personalised recommendations