On a deformation sign for identifying defects on the basis of the analysis of the forms of the natural vibrations of a cantilever with a notch

Abstract

A method for determining the location and depth of a notch has been developed on the basis of the results of a finite-element analysis of natural vibration modes of a cantilever with a notch. A phenomenological relationship is obtained that relates the degree of cantilever damage to the characteristic features of its natural vibration modes. A new diagnostic sign of the degree of cantilever damage is proposed, which is the angle between the tangents on the plot of the natural form of the fourth vibration mode. An approximate equation is deduced that describes the dependence of the angle between the tangents at the “break” point of the shape of the fourth vibration mode on the depth of a notch in the cantilever.