Comparative vibration study of EN 8 and EN 47 cracked cantilever beam

Since earlier days, most of the failures encountered by the structures or machines are mainly due to material fatigue. The dynamic behaviour of the beam may change when cracks begin to appear in it. Knowledge of these changes in the dynamic individualism is important in crack detection as well as in structure or in machine design. This paper deals with systematic study on the free vibration of Euler-Bernoulli beam containing open edge transverse cracks. In this study, two springs steel materials (EN 8 and EN 47) are considered. The effect of the top side cracks and bottom side cracks on the natural frequency of a cantilever beam is discussed. The natural frequency of a cracked case cantilever beam is investigated numerically using FE analysis software ANSYS. Experimental work is done by using DeweFRF to investigate the natural frequency of cracked beams for strong validation of the numerical results. The results of this study suggest that the average value of natural frequencies for all top side cracked beams are identical to the average value of natural frequency for all bottom side cracked beams. This is true for both EN 47 and EN 8. Hence, it is clear that the dynamic characteristic (natural frequency) is not changing, when same configuration of cracks is either on top or bottom side of the beam. The natural frequencies for EN 8 material are comparatively on higher side than EN 47 material for the same crack configurations. In most of the cracked cases, the damping effect of EN 47 is greater than EN 8. It is also found that as crack location increases at constant crack depth, then natural frequency increases. At the last location, as crack depth increases, natural frequencies almost remain same. It is observed that, the presence of top side crack and bottom side crack of the same configuration in the cantilever beam is not a function of natural frequency, when cantilever beam is of a square cross section

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

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

STUDY OF FREE UNDAMPED AND DAMPED VIBRATIONS OF A CRACKED CANTILEVER BEAM

This paper deals with the analytical study on the free un-damped and damped vibration of Euler–Bernoulli beam containing edge cracks. In this study, the effects of the different crack parameters such as crack depth, crack location and crack angle on the dynamic responses of the beam are discussed. Research studies presented the effect of transverse cracks on the natural frequency. Earlier studies have not considered the effect of oblique cracks on the cantilever beam. Presence of cracks in various parts of machine changes its vibration parameters to a considerable degree i.e. natural frequency and damping factor. In this paper, the transverse cracks and oblique cracks are considered on a cantilever beam at different locations and depths to study its effects on the various vibration parameters. The information of the dynamic response i.e. changes in the natural frequency, is much needed in the health monitoring of the beam to determine the location and depth of the crack in the beam. The response of a cracked cantilever beam for a damping factor has been studied by the combination of finite element analysis and theoretical method. Tests were conducted on the cantilever beam for both an intact and cracked cases by using FFT Analyzer. ANSYS software is used to validate the experimental results. The results of this study suggest that the natural frequency of the beam decreases significantly, when crack depth increases to 80% of the depth of the beam and it is least affected, when depth of the crack is either 20% or less than 20% of the depth the beam. Further it is also observed that the value of damping factor is least affected when crack remains present in the beam more towards the free end, when compared to damping factor of an intact beam

Paradigm for natural frequency of an un-cracked simply supported beam and its application to single-edged and multi-edged cracked beam

In this research paper, a theoretical method of analysis of the first natural frequency of an un-cracked simply supported beam in bending mode is presented. The formula of a paradigm is used to determine the natural frequency of an un-cracked beam. The converged natural frequency formula of a paradigm is then extended to a single edged and multi-edged cracked simply supported beam to evaluate their natural frequency. The main attraction of the proposed method is that it gives one more significant way to the researchers to determine the natural frequency of cracked beams. The limited fatigue strength, defects like corrosion, corrosion-erosion, and corrosion fatigue in the beam are the main causes of formation of edged cracks in beams. Hence the evaluation of natural frequency of cracked beams and its use in the inverse problem is of utmost importance to do the condition monitoring of the structures by the vibration methods