Multi-cracked shear deformable beams under moving loads

The case of moving load along the axis of continuous beams has been subject of attention in the literature in view of various applications mainly oriented to analyse the effect of vehicular traffic along a bridge span. The above studies become even more significant when the beam span is hindered by the presence of concentrated cracks causing a prejudicial increase of the deformability. Various approaches have been proposed in the literature for the analysis of single as well multi-cracked beams when travelled by moving loads. Despite the large number of papers devoted to the analysis of moving loads, very few of them consider the case of shear deformable beams in presence of multiple cracks. Thereby, this study addresses the first order Timoshenko theory in presence of multiples cracks subjected to a concentrated moving load. Recently, the authors proposed a distributional approach to treat the Timoshenko-Ehrenfest multi-cracked beam model and provided an extended modal analysis to solve the case of stationary (time constant position) impulsive loads, as well as loads with time varying intensity. The key point of the proposed approach is represented by the formulation of the orthogonality conditions for the distributional modal eigenvectors including the effect of multiple cracks by means of suitable distributional terms. On this ground, the present study provides the extension of the above distributional extended modal superposition analysis to the case of loads whose position is varying in time suitable to evaluate the dynamic effect of a concentrated moving load along the beam axis.