The influence of concentrated damage in the dynamic behaviour of framed structures

In this work a model of the Timoshenko beam in presence of singularities along the span is presented. The adopted model allows the formulation of exact closed form solutions of the response in presence of static loads. The latter closed form expressions of the response parameters avoid the enforcement of any continuity conditions at the crosssections with the singularities. Among the possible singularities, the case of concentrated cracks is treated and the presented closed form solutions are exploited to formulate the displacement shape functions of the beam and the relevant stiffness matrix. The presented beam model is adopted for a finite element discretisation of damaged framed structures. In particular, by means of the introduction of a mass matrix consistent with the adopted shape functions, the presented model allows the dynamic analysis of framed structures in presence of concentrated cracks. Extensive numerical applications to 3D frames are presented with particular regard to the influence of the cracks on the dynamic response parameters.