The influence of the axial force on the vibration of damaged frames

In this paper the dynamic stiffness matrix of an Euler-Bernoulli beam-column in the presence of an arbitrary number of concentrated cracks is derived. The procedure adopted is based on the availability of the explicit solution of the vibration modes of the multi–cracked beam-column, recently derived by the authors in a previous paper. The knowledge of the exact dynamic stiffness matrix of the multi–cracked beam-column allows the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures axially loaded. The great advantage of the proposed approach is that the degrees of freedom of the overall damaged frame structure are exactly the same as those of the equivalent undamaged structure regardless of the number of concentrated damages. Numerical results, aimed at showing the advantages of the proposed approach and at validating the obtained solution, are reported.