Harmonic Vibration and Resonance Effects in the Case of Longitudinal Shear of a Hollow Cylinder with Crack

We propose an efficient analytic-numerical method for the evaluation of dynamic stresses in a hollow cylindrical body of arbitrary cross section with a through crack under the conditions of antiplane deformation. This method enables us to separately solve the integral equations on the surface of the defect and satisfy the conditions of harmonic loading on the boundary of the body. We deduce the formulas for the dynamic stress intensity factors in the vicinity of the crack and study the influence of its geometric parameters and the frequency of vibration on the indicated factors, in particular, with the evaluation of resonance frequencies.