Engineering Transactions, 17, 3, pp. 435-450, 1969

Rozprzestrzenianie się fal w sprężystym ortotropowym walcu kołowym

M. Kozarow


TS. P. Iwanow


In the following article the propagation of elastic waves of the type (1.1) in an infinite orthotropic circular cylinder is investigated. That is the most-general case of cylindrical anisotropy, for which the propagation of waves of this type is possible. The solutions of the unknown functions U(r), V(r), W(r) are determined in the form of generalized power series, convergent for every r = 0. For some meanings for the elastic constants by given v it is possbile to receive solutions, having logarithmic singularities for r = 0, The boundary conditions the cylindrical surface to be free from loading, can always be satisfied for a hollow cylinder, whereas by a solid cylinder that is possible only for some orthotropic materials, for which the elastic constants satisfy some additional inequalities, depending on v. Determined are the cases. frequency equations in the general case as well as some interesting particular.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


L. POCHHAMMER, Über Fortpflanzungsgeschwindigkeiten kleiner Schwingungen, J. Rein. Angew. Math., 81 (1876), 324-336.

C. CHREE, The equations of an isotropic solid in polar and cylindrical coordinates, Trans. Camb. Phil. Soc., 17 (1889), 250.

H. KOLSKY, Stress Waves in Solids, Oxford 1953.

C. CHREE, On longitudinal vibrations of aleotropic bars with one axis of material symmetry, Quart. J. Math., 24 (1890), 340-358.

I. MIRSKY, Wave propagation in transversely isotropic circular cylinders, J. Acoust. Soc. America, 6, 37 (1965), 1016-1026.

J.L. NOWINSKI, Propagation of longitudinal waves in circular cylindrically orthotropic bars, Trans. of ASME, Ser. B, 3, 89 (1967), 408-412.

7. П. И. Берштейн, ВОАНЫ кручения в анизотропном неоднородном цылиндрическом стержне,

Инж. Ж., 3, 5 (1965), 572-574.

H. N. ABRAMSON, H.J. PLASS, E.A. RIPPERGER, Stress waves propagation in rods and beams, Advances Appl. Mech., 5 (1958), 11-194.

Л, Аикола, У. Нигул, Волновые процессы деформации упругих плит и оболочек, Изв. АН УССР, Серия, физико-мат. и мех. наук., № 1, 1965.

E. KAMKE, Differentialgleichungen-Lösungsmethoden und Lösungen, Leipzig 1959.