Free Vibration of Damaged Beam Structure with a Notch Defect
In this paper, we derive the universal expression of the modal parameters for a damaged beam under arbitrary boundary conditions. The delta function is first employed to describe a notch damage in the beam and consequently to derive the governing equation for the damaged beam. Second, by virtue of the perturbation method, the eigenvalues and the corresponding mode shapes are obtained for the damaged beam. Finally, numerical examples are given for an elastically supported beam. It is believed that the proposed approach could provide the necessary theoretical background for damage identification in beam structures.
Chunliang Zhang and Paul P. Lin
J. Y. Chen et al., "Free Vibration of Damaged Beam Structure with a Notch Defect", Applied Mechanics and Materials, Vols. 226-228, pp. 44-47, 2012