Vibration-Based Diagnostics of Transverse Surface Cracks in Rods of Different Cross Section Under Longitudinal Vibrations

The paper considers the results of determining the vibrodiagnostic indicators of the presence of various mode I breathing transverse cracks in rod elements of rectangular and circular cross section with different boundary conditions under longitudinal vibrations. Relative second harmonic amplitudes in the vibration spectrum at the main and superharmonic resonance of the first eigenmode of cantilever rods without mass and with a mass at the end and rods with the ends free for longitudinal displacements under forced and kinematic vibration excitation were taken as diagnostic indicators. To determine the above indicators, analytical and numerical bending vibration methods considered before are used. In the analytical solution, the nonlinearity parameter of the vibrating system is calculated using the corresponding values of stress intensity factors. The numerical solution is performed on the basis of eight-node finite element models with the representation of a breathing crack as a mathematical cut and the treatment of a contact problem in the formulation providing mutual nonpenetration between crack faces. Plots of the values of diagnostic indicators as a function of relative crack depth, crack location and the site of measurement of longitudinal displacements have been obtained. Comparisons of values of diagnostic indicators with the value of relative change in natural vibration frequency are presented. It has been shown that at the main resonance, the numerical solution confirms the pronounced effect of localization of diagnostic indicators in the crack region. It has been found that at the superharmonic resonance, the value of the vibrodiagnostic indicator is two orders of magnitude higher than that of the indicators at the main resonance, but the effect of their localization near the crack does not practically manifest itself. Some localization is observed for the absolute values of the second harmonic, and only for longitudinal strain, there is a strongly pronounced effect. A comparison of the obtained values of diagnostic indicators with the data for bending vibrations is given. It is noted that in spite of basically lower indicators under longitudinal vibrations, they have an advantage in terms of the possibility to diagnose symmetric both surface and internal breathing cracks.