The influence of the axial force on the vibration of the Euler-Bernoulli beam with an arbitrary number of cracks

The exact closed-form solution for the vibration modes and the eigen-value equation of the Euler-Bernoulli beam-column in the presence of an arbitrary number of concentrated open cracks is proposedevaluated. The solution is provided explicitly as functions of four integration constants only, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads the exact evaluation of the vibration frequencies as well as the buckling load of the beam beam-column and the corresponding eigen-modes. Furthermore, the presented solution allows a comprehensive evaluation of the influence of the axial load on the modal parameters of the beam. The cracks, that are, not subjected to the closing phenomenon,, are modellled as a sequence of Dirac’s delta generalisedgeneralised functions in the flexural stiffness. The eEeigen-mode governing equation is formulated over the entire domain of the beam without enforcement of any further continuity condition. The influence of the axial load oin the vibration modes of beam-columns with different number and position s of cracks, under different boundary conditions, have been analisedanalysed by means of the proposed closed-form expressions. The presented parametric analysis highlightsing some abrupt changes of the eigen-modes and the corresponding frequencies.