The dynamical stress concentration near a spherical crack in a twice-truncated elastic cone

摘要

Engineering practice demands the solving of the inverse problems of fracture mechanics, with this aim, it is necessary to get an analytical solution of the corresponding direct problem. So, in this paper, research was made considering a twice-truncated elastic cone with a spherical crack inside in steady state torsional oscillation. As a result of the problem solving the eigen frequency values and dynamical stress intensity factor were investigated for different parameters of the cone and crack. The boundary resonance effect was found and analyzed; this gives the opportunity to use the derived results during nondestructive testing of the elastic body. The solution is constructed as the superposition of a continuous solution (the problem for an elastic cone without a crack under dynamical torsion), and a discontinuous one (the problem for a spherical crack). The former solution was derived with a great contribution from the G. Ya. Popov results [G. Ya. Popov, 1982]. The wave field of an elastic twice truncated cone was investigated. The eigen frequencies were calculated for different cone's and crack's geometrical parameters. The investigation demonstrated the fact of boundary resonance which is commonly used in the inverse problems of fracture mechanics.