Health Monitoring of Cantilever Rod Using Vibration Test "Theoretical and Numerical Study"

The aim of this study is to assess the numerical analysis by using a theoretical model for detecting cracks on cantilever rod. A theoretical model for the cantilever rod was based on the Euler-Bernoulli beam theory. The theoretical model was used to calculate the natural frequency for the uncracked rod, as well as for the cracked rod. The effect of the crack on the natural frequencies was inserted by using the second moment of inertia for the cracked cross section, where it influenced the natural frequency and led to decrease the stiffness of the cracked beam. The theoretical results showed that the reduction in natural frequencies (RFI) was a good indicator for detecting the damage magnitude. A finite element model for a cantilever solid rod was created. The Eigen analysis was conducted to determine the dynamic properties (natural frequency and mode shape). The crack detection was performed by monitoring the changes in the first four natural frequencies. It is hypothesized that as the natural frequency of a structure is directly corresponded to its stiffness, the monitoring of any changes exhibited in the natural frequency can lead to the detection in the change of the stiffness of the structure. The mass was assumed constant because the amount of lost due to crack was very less, hence it was neglected. The theoretical model and natural frequency's results were in good agreement with numerical results.