Torsion problem for an elastic twice-truncated cone

Abstract

The problem of an elastic twice-truncated cone wave field estimation is investigated in case of steady state torsional oscillations. The G. Ya. Popov integral transform with regard to an angular coordinate is applied. Thus reducing the original problem to one-dimensional boundary value problem in the transform's domain. The Green's function is build for onedimensional boundary value problem. With it's help the solution of one-dimensional problem is constructed in an explicit form. The G. Ya. Popov inverse transformation helped to derive the solution in original domain in form of an infinite sum. With it's help dependence of the eigenfrequencies from the cone's geometric parameters is investigated. Stress field was found with the use of asymptotic procedure. Comparison plots are build for different opening angles. MSC: 74G70, 74H99, 74J10.