Geodesic
Wave propagation in fibre-reinforced cylinders
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 58-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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Non-stationary wave propagation in cylindrical composite shell is considered. The shell consists of isotropic matrix reinforced by two families of symmetrically wound spiral fibres. These families have the same mechanical properties and the cylinder is considered to be incompressible. Solutions of coupled equations of motion are represented in the form of Frobenius power series. Approximate dispersion relation derived is analyzed numerically for different shell thicknesses and fibre winding angles. 
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R. R. Mukhomodyarov; Ya. A. Parfenova. Wave propagation in fibre-reinforced cylinders. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 58-62. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a9/

[1] Gazis D. C., “Three-dimensional investigation of the propagation of waves in hollow circular cylinders. I. Analytical Foundation”, J. Acoust. Soc. Amer., 31 (1959), 568–573 | DOI | MR

[2] Kossovich L. Yu., Nestatsionarnye zadachi teorii uprugikh tonkikh obolochek, Izd-vo Sarat. un-ta, Saratov, 1986, 176 pp.

[3] Mekhtiev M. F., Fomina N. I., “Svobodnye kolebaniya transversalno-izotropnogo pologo tsilindra”, Mekhanika kompozit. materialov, 38:1 (2002), 81–98 | MR

[4] Mirsky I., “Axisymmetric vibration of orthotropic cylinders”, J. Acoust. Soc. Amer., 36 (1964), 2106–2112 | DOI | MR

[5] Ohnabe H., Nowinski J. L., “On the propagation of flexural waves in anisotropic bars”, Ing.-Archiv., 40 (1971), 327–338 | DOI | Zbl

[6] Shuvalov A. L., “The frobenius power series solution for cylindrically anisotropic radially inhomogeneous elastic materials”, J. Mech. Appl. Math., 56:3 (2003), 327–345 | DOI | MR | Zbl

[7] Spencer A. J. M., Deformations of fibre-reinforced materials, Clarendon Press, Oxford, 1972 | Zbl

[8] Nayfeh A. H., “The general problem of elastic wave propagation in multilayered anisotropic media”, J. Acoust. Soc. Amer., 89 (1991), 1521–1526 | DOI