APPRAISING THE ACCURACY OF A NOVEL MODEL FOR L-SHAPED CRACKS

Abstract

In the current paper we aim to evaluate the accuracy of a previously developed method to determine the frequency drop of a cantilever beam having an L-shaped damage with a well-defined position and size. The method is based on the fact that the deformation energy lost by reducing a section of the beam is proportional to the deflection of the same beam under own mass. By setting the boundary and initial conditions for the cantilever, fixed at one end and free at the other, we applied equations of motion for the entire structure based on the Euler-Bernoulli beam model. By using the relation between the frequencies and the deformation energy we obtained a correction term that allows us to calculate the natural frequencies of the cantilever beam having a reduced section based on the frequencies of the undamaged beam. The method is applied through a program developed in the Python language by our research team. The obtained frequencies for the beam with a reduced section are compared with does deducted with the help of the ANSYS simulation software for the beam with an L-shaped crack. Tests performed to find the accuracy of the frequency estimates show that the results are very accurate and we concluded that this method can be used with confidence for modal analysis issues.