Study of vibrations in structural components with presence of cracks

Abstract

The mechanical and structural components, due to the presence of cracks, are susceptible to failure in service; causing catastrophic and irreversible damage. This work focuses on the study of an analytical crack identification method based on the measurement of natural frequencies of vibration. By applying the calculus of variations, the exact solution of the problem of vibrations of Euler Bernoulli beams of constant section and isotropic and homogeneous material was obtained. An analytical method for the detection of cracks in beams was developed. It consists of solving the inverse problem of obtaining the position and depth of the fissure, from knowing the first 3 values of the dimensionless coefficient of frequencies. A sensitivity analysis of the method was performed for the articulated-articulated condition, considering a maximum uncertainty in the measurement of the frequency of 2%. The results presented allow to determine the detection capacity of the method, for any location and depth.