VIBRATIONS OF A THIN-WALLED STRUCTURE CONSTRUCTED FROM ORTHOTROPIC ELASTIC NON-CLOSED CYLINDRICAL SHELLS WITH FREE AND SIMPLE SUPPORT BOUNDARY CONDITIONS AT THE EDGE GENERATORS

Abstract

The problem of existence of natural vibrations of an elastic orthotropic thin-walled structure constructed from circular non-closed infinite cylindrical shells with free and simple support boundary conditions on the edge generators and an elastic orthotropic thin-walled structure constructed from circular non-closed finite cylindrical shells with free and simple support Navier’s boundary conditions at the edge generators, which have a simple support on the boundary directional curves, are studied. Using the system of equations of the related classical theory of orthotropic cylindrical shells dispersion equations and asymptotic formulas are obtained for determining the eigenvalue frequencies of possible vibration types for the corresponding thin-walled structures. An algorithm for separating the possible vibrations is presented. Approximate values of dimensionless characteristics of eigenvalue frequencies and fading characteristics of the related vibration forms are given for the cases of orthotropic thin-walled structures constructed from various numbers of identical circular non-closed finite cylindrical shells.