The influence of damage on the eigen-properties of Timoshenko spatial arches

This paper studies the influence of concentrated damage on the eigen-properties of Timoshenko curved beams. Either single spatial arches or frame dome structures, obtained as assemblage of circular Timoshenko arches, are considered in presence of single or multiple damage and their exact dynamic stiffness matrices are evaluated. The natural frequencies and the corresponding modes of vibration are exactly calculated by means of a numerical strategy based on the Wittrick & Williams algorithm. The proposed procedure allows evaluating the effects of damage positions and intensities on the eigen-properties of the considered arch structures and to observe that, in the case of arches, the effects of damage severity and its location cannot be rigorously uncoupled. This latter result appears to be in contrast to what obtained in the literature for beams and rods. Since the adopted numerical approach leads to exact solutions, the obtained results can also be used as benchmarks for validating approximate numerical FEM strategies of Timoshenko damaged curved beams.