A direct based method with an analytical capability parameter to detect open cracks on free vibrating beams

Abstract

This paper presents analysis of a mechanical system composed of free vibration of an Euler-Bernoulli beam with an open crack. Two new proposals have been presented to analyse such systems: a direct crack identification method to obtain the crack properties and a theoretical margin of detection parameter to quantify the capability of the theoretical model used to detect a single crack. The direct crack identification method uses first three natural frequencies of a cracked beam to obtain the unknown crack location and depth without solving the inverse vibration problem. On the other hand, the theoretical margin of detection parameter provides capability to the analytical model to detect the location and depth of an open crack using the first three natural frequencies as a function of crack location and depth for different end conditions. To show the robustness of the direct crack identification method, errors on the first three exact values of the natural frequency parameters of the cracked beam are induced before applying the proposed method and the resulting errors were calculated. Contour plots have been developed for classical and elastically restrained end conditions to predict the detectable zones as a function of crack location and depth. The proposed analysis has been carried out on the widely used closed-form solution of the beam model.