Behavior of cracked Euler–Bernoulli beam and inverse problem for assessing crack severity

Abstract

In this present study, natural frequencies of the first two modes of bending vibration for the cracked simply supported Euler–Bernoulli beam is determined using finite element analysis (FEA). FEA natural frequencies for the cracked beam are used to investigate the behavior of the cracked beam and also used in the inverse problem of crack depth detection. Dynamic behavior of the cracked simply supported beam is observed, and it is found that normalized mode shape at crack location has great effect on amount of decreasing of natural frequencies. When normalized mode shape at crack location is increased, then natural frequencies decrease. In this study, pattern of mode shape played a vital role in decreasing or increasing natural frequencies. At the midpoint of the beam, there is largest bending moment in first bending mode and there is nodal point in second bending mode. Harmonic analysis for the cracked simply supported beam is carried out to find von Mises stress responses and appearance of peaks at frequency of first bending mode is noticed in graphs of von Mises stress response, expressing high values of von Mises stress at crack tip. Inverse problem of assessing the crack depth is performed using results of FEA first mode frequency ratio and published experimental results and the method showed good results in case of high crack depth ratios.