• Shell vibrations;
  • asymptotic formulae;
  • dispersion equations.


The problem of existence of localized natural vibrations of an elastic orthotropic solid thin-walled structure consisted of identical circular non-closed infinite (finite) cylindrical shells with free and rigid-clamped boundary conditions at the edge generators is studied. In the case of finite cylindrical shells the boundary directional curves are hinge-mounted. Using the system of equations of the related classical theory of orthotropic cylindrical shells, dispersion equations, and asymptotic formulae for determining the eigenfrequencies of possible vibration types of the corresponding thin-walled structures are derived. An algorithm for separating the possible vibrations is presented. Approximate values of dimensionless characteristics of eigenfrequencies and damping characteristics of the related vibration forms are given for the cases of orthotropic solid thin-walled structures constructed of different number of identical circular non-closed finite cylindrical shells. Comparative study of the approximate method given in this paper with the Abramov's method of transfer with orthogonalization confirmed the correctness and effectiveness of the approximate method.