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.
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References
Armenàkas, A. E. (1967): Propagation of harmonic waves in composite circular cylindrical shells. Part I—Theoretical investigation. AIAA 9, 599–605
Armenàkas, A. E. (1971): Propagation of harmonic waves in composite circular cylindrical shells. Part II—Numerical analysis. AIAA 5, 740–744
Armenàkas, A. E.; Gazis, D. C.; Herrmann, G. (1969): Free vibrations of circular cylindrical shells. New York: Pergamon Press
Babero, E. J.; Reddy, J. N.; Teply, J. L. (1990): General two-dimensional theory of laminated cylindrical shells. AIAA 28, 544–553
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, 568–578
Huang, K. H.; Dong, S. B. (1984): Propagating waves and edge vibrations in anisotropic composite cylinders. J. Sound Vibr. 96, 363–379
IMSL Library (1984): Fortran subroutine for mathematics and statistics. Edition 9.2. Texas: IMSL Inc.
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, 411–418
Kundu, T.; Mal, A. K. (1985): Elastic waves in a multilayered solid due to a dislocation source. Wave Motion 7, 459–471
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 York
Moore, I. D. (1990): Vibration of elastic and viscoelastic tubes. I—Harmonic response. J. Eng. Mech. 116, 928–942
Muller, D. E. (1956): A method for solving algebraic equations using an automatic computer. Mathematical Tables and Aids to Computation 10, 208–215
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.
Nelson, R. B.; Dong, S. B.; Kalra, R. D. (1971): Vibrations and waves in laminated orthotropic circular cylinders. J. Sound Vib. 18, 429–444
Onoe, M.; McNiven, H. D.; Minlind, R. D. (1962): Dispersion of axially symmetric waves in elastic rods. J. Appl. Mech. 729–734
Pochhammer, L. (1876): Ueber die Fortpflanzungsgeschwindigkeiten von Schwingungen in einem unbegrenzten isotropen Kreiscylinder. Z. Math. 81, 324–336
Rattanawangcharoen, N.; Shah, A. H.; Datta, S. K. (1992): Wave propagation in laminated composite circular cylinders. Int. J. Solids Struct. 29, 767–781
Sun, C. T.; Whitney, J. M. (1974): Axisymmetric vibrations of laminated composite cylindrical shells. J. Acoust. Soc. Am. 55, 1238–1246
Walfram, S. (1988): Mathematics, A system of doing mathematics by computers. The Advanced Book Program. Reading, Mass.: Addisson-Wesley
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Communicated by S. N. Atluri, December 17, 1991
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Rattanawangcharoen, N., Shah, A.H. Guided waves in laminated isotropic circular cylinder. Computational Mechanics 10, 97–105 (1992). https://doi.org/10.1007/BF00369854
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DOI: https://doi.org/10.1007/BF00369854