Computational Mechanics

, Volume 10, Issue 2, pp 97–105 | Cite as

Guided waves in laminated isotropic circular cylinder

  • N. Rattanawangcharoen
  • A. H. Shah
Article

Abstract

This paper investigates, analytically and numerically, the dispersion characteristics of a laminated isotropic circular cylinder. The propagator matrix, which relates the stresses and displacements of one interface of a layer to those of another interface, is formulated based upon the three-dimensional theory of elasticity. The dispersion relation of the cylinder is implicitly established from this propagator matrix. The numerical evaluation is carried out by the Muller's method with an initial guess from a Rayleigh-Ritz type approximate method. Examples of an elastic rod and a two layered isotropic cylinder are presented and discussed to illustrate the accuracy and effectiveness of the method.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armenàkas, A. E. (1967): Propagation of harmonic waves in composite circular cylindrical shells. Part I—Theoretical investigation. AIAA 9, 599–605Google Scholar
  2. Armenàkas, A. E. (1971): Propagation of harmonic waves in composite circular cylindrical shells. Part II—Numerical analysis. AIAA 5, 740–744Google Scholar
  3. Armenàkas, A. E.; Gazis, D. C.; Herrmann, G. (1969): Free vibrations of circular cylindrical shells. New York: Pergamon PressGoogle Scholar
  4. Babero, E. J.; Reddy, J. N.; Teply, J. L. (1990): General two-dimensional theory of laminated cylindrical shells. AIAA 28, 544–553Google Scholar
  5. Gazis, D. (1959): Three-dimensional investigation of the propagation of waves in hollow circular cylinders. I—Analytical foundation and II—Numerical results. J. Acoust. Soc. Am. 31, 568–578Google Scholar
  6. Huang, K. H.; Dong, S. B. (1984): Propagating waves and edge vibrations in anisotropic composite cylinders. J. Sound Vibr. 96, 363–379Google Scholar
  7. IMSL Library (1984): Fortran subroutine for mathematics and statistics. Edition 9.2. Texas: IMSL Inc.Google Scholar
  8. Karunasena, W. M.; Bratton, R. L.; Datta, S. K.; Shah, A. H. (1990): Elastic wave propagation in laminated composite plates. ASME J. Eng. Mat. Tech. 113, 411–418Google Scholar
  9. Kundu, T.; Mal, A. K. (1985): Elastic waves in a multilayered solid due to a dislocation source. Wave Motion 7, 459–471Google Scholar
  10. Mason (1968): Guided wave propagation in elongated cylinders and plates. Meeker, T. R. and Meitzler, A. H. (eds): Physical Acoustics, Vol. 1, Part A; pp. 111–167: Academic Press Inc.: New YorkGoogle Scholar
  11. Moore, I. D. (1990): Vibration of elastic and viscoelastic tubes. I—Harmonic response. J. Eng. Mech. 116, 928–942Google Scholar
  12. Muller, D. E. (1956): A method for solving algebraic equations using an automatic computer. Mathematical Tables and Aids to Computation 10, 208–215Google Scholar
  13. National Bureau of Standards (1964): Handbook of mathematical functions with formulas, graphs, and mathematical tables. Abramowitz, M. and Stegun, I. A. (eds): Applied Mathematics Series 55: Washington D.C.Google Scholar
  14. Nelson, R. B.; Dong, S. B.; Kalra, R. D. (1971): Vibrations and waves in laminated orthotropic circular cylinders. J. Sound Vib. 18, 429–444Google Scholar
  15. Onoe, M.; McNiven, H. D.; Minlind, R. D. (1962): Dispersion of axially symmetric waves in elastic rods. J. Appl. Mech. 729–734Google Scholar
  16. Pochhammer, L. (1876): Ueber die Fortpflanzungsgeschwindigkeiten von Schwingungen in einem unbegrenzten isotropen Kreiscylinder. Z. Math. 81, 324–336Google Scholar
  17. Rattanawangcharoen, N.; Shah, A. H.; Datta, S. K. (1992): Wave propagation in laminated composite circular cylinders. Int. J. Solids Struct. 29, 767–781Google Scholar
  18. Sun, C. T.; Whitney, J. M. (1974): Axisymmetric vibrations of laminated composite cylindrical shells. J. Acoust. Soc. Am. 55, 1238–1246Google Scholar
  19. Walfram, S. (1988): Mathematics, A system of doing mathematics by computers. The Advanced Book Program. Reading, Mass.: Addisson-WesleyGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • N. Rattanawangcharoen
    • 1
  • A. H. Shah
    • 1
  1. 1.Department of Civil EngineeringUniversity of ManitobaWinnipegCanada

Personalised recommendations