Approximate analytical method for determining the vibration-diagnostic parameter indicating the presence of a crack in a distributed-parameter elastic system at super- and subharmonic resonances

An approximate method for calculating the vibration-diagnostic parameter indicating the presence of a crack in an elastic distributed-parameter system at super- and subharmonic resonances is considered. The method involves the finding of the non-linearity characteristic of an elastic system based on the analysis of its forced vibrations in the undamaged state and the use of results of the approximate analytical determination of parameters of nonlinearity for vibrations of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force at the above-mentioned resonances.