Vibration of beams with multiple open cracks subjected to axial force

A new method is proposed to obtain the eigenfrequencies and mode shapes of beams containing multiple cracks and subjected to axial force. Cracks are assumed to introduce local flexibility changes and are modeled as rotational springs. The method uses one set of end conditions as initial parameters for determining the mode shape functions. Satisfying the continuity and jump conditions at crack locations, mode shape functions of the remaining parts are determined. Other set of boundary conditions yields a second-order determinant that needs to be solved for its roots. As the static case is approached, the roots of the characteristic equation give the buckling load of the structure. The proposed method is compared against the results predicted by finite element analysis. Good agreement is observed between the proposed approach and finite element results. A parametric study is conducted in order to investigate the effect of cracks and axial force levels on the eigenfrequencies. Both simply supported and cantilever beam-columns are considered. It is found that eigenfrequencies are strongly affected by crack locations, severities and axial force levels. Simple modifications to account for flexible intermediate supports are presented as well. The proposed method can efficiently be used in detecting crack locations, severities and axial forces in beam-columns. Furthermore it can be used to predict the critical load of damaged structures based on eigenfrequency measurements.

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