Interaction of a Crack with Inclusion in a Cylindrical Body Under Longitudinal Shear Vibrations

We solve the problem of determination of the stress state of an infinitely long cylinder of an arbitrary cross section under the conditions of longitudinal shear vibrations in the presence of interaction between through defects (a crack and a thin rigid inclusion). We use a method that enables one to satisfy the conditions imposed on the surfaces of defects and the boundary conditions of time-harmonic loading. We propose approximate formulas for the evaluation of stress intensity factors with the help of which we investigate the influence of the geometric parameters of cross section of the cylinder on the values of resonance frequencies.