Free vibration study of v-shape and rectangular shape double-sided cracks in a cantilever beam

Abstract

The vibration response of a structural member changes due to the presence of crack because crack introduced local flexibility in it. Depending upon the vibration amplitude the crack may be of open or close type. Crack gives catastrophic failure to the structure hence it is very crucial to understand the dynamic of the structure. In the inverse problem, vibrating properties like natural frequency, resonance amplitude can be used as a basic criterion in crack detection or in design of structures. Previously, a mathematical model was developed by W. M. Ostachowicz and M. Krawczuk for the cantilever beam which has two open double-sided v-shape cracks. This model is used to find the natural frequency and characteristics roots in bending mode. The aim of this study is to prove whether the developed mathematical model can be used for rectangular shape cracks because in various applications existence of v shape and rectangular shape cracks are very general. For this reason, results of v-shape cracked cases are used as a reference model. Modal analysis is done by using ANSYS software to get the pure bending natural frequencies of the various cracked cases. Then the same mathematical model is used for rectangular shape cracked cases to calculate the characteristics roots. The value of characteristics roots obtained for a v-shape crack by W. M. Ostachowicz and M. Krawczuk and a rectangular shape crack cases studied are in good agreement. Hence it proves the flexibility of the model developed with v-shape cracks. In addition to this, the effect of two double-sided cracks on the characteristics roots is studied for all the cracked cases given in the reference model. It is found that as crack depth increases at any unique location then natural frequency decreases. At last location even though crack depth increases value of natural frequency almost remains constant.