Influence of Concentrated Cracks on Framed Structures by Means of the Dynamic Stiffness Method

In the paper the free vibration of Euler-Bernoulli beams in presence of an arbitrary number of concentrated cracks are analyzed through the dynamic stiffness matrix method. The procedure for the evaluation of the exact dynamic stiffness matrix of a beam is based on the exact closed form solution of the vibration modes of the multi-cracked beam, derived by the same authors in a previous paper. The knowledge of the dynamic stiffness matrix of the damaged beam allows the derivation of the dynamic stiffness matrix of framed structures in presence of concentrated damages and the evaluation of the exact vibration frequencies and the corresponding mode shaped, through the application of the general Wittrick and Williams algorithm. In the paper an application for the evaluation of natural frequencies and the corresponding mode shapes of a simple framed structure in presence of concentrated cracks is reported.