Libov D. On the spectrum of natural frequencies of a cylinder of finite length

The solution to the problem of propagation of normal waves in an elastic isotropic cylindrical waveguide with a free surface, obtained by the method of separation of variables, and the solution to the corresponding dispersion equation serve a basis for describing the eigen vibrations of a corresponding finite cylinder. The investigations involve the solution by means of the superposition method to the first boundary-value problem of elasticity theory about vibrations of cylinder, induced by a non-axisymmetric load at the ends. The algorithm to the analytical solution to the infinite system of the equations, corresponding to the boundary-value problem, provides the possibility to study an eigen-value spectrum. Investigation of non-axisymmetric modes reveals that two lines, lying below the critical frequency of the waveguide, exist in an eigen frequency spectrum irrespectively to Poisson's ratio. These spectral curves, corresponding to the symmetric and antisymmetric vibrations, are tended to the end resonance frequency of a semi-infinite waveguide in an oscillation manner and practically coincide for a sufficiently long cylinder.