The Application of Modal Analysis to the Identification o f the Relationships between the Dynamic Proper ties and Crack Parameter s of the Eul er–Bernoulli Beams

In the past two decades, modal analysis has been prevalently used in determining and optimizing the dynamic properties of the engineering structures. The recent advancements in this area have led to the evolution of experimental model ing. A large fraction of these evolutionswas driven by the advancements caused by the fast Fourier transform (FFT) analyzers . The modal analysis is the process of defining the dynamic properties of a system in terms of its natural frequency, damping coefficients, and mode shapes. This analysis is aimed at developing a mathematical model of the system dynamic response. In the present research, the vibration modes of a n aluminum cantilever with a central discrete crackwere compared to the vibration m odes of an unsupported (free-free) st eel beam with several cracks of varying depths. Afterwards, the corresponding freque ncy spectra were recorded by stimulating the n odal points with a modal impact ha mmer. Following the theoretical calculation of the natural frequencies of the beam a nd a comparison of the results with the experimental results, a strong correlation was observed between the results. In addition, the mod e shapes of the specimens with failure cracks were similar to the experimental results. Therefore, the capacity of the modal analysis method for the identification of t he relations between the dynamic properties and the crack parameters was approved.

Keywords:

modal analysis , Euler–Bernoulli beam , resonant frequency , fr equency spectrum