| Popis: |
Damage in beams can strongly affect their dynamic properties and consequently their response. On the other hand, the correct evaluation of the damage intensity is a problem of difficult solution. For these reasons, exploring the variability of the dynamic response in damaged beams considering the damage intensities as uncertain parameter is a useful contri-bution to assess the safety of structures. Classic approaches require to treat damage as con-centrated rotational springs, where continuity conditions have to be enforced, and to perform re-analyses varying the damage intensities in a desired range. In this paper, two main improve-ments to this procedure are provided. The first contribution is the use of an efficient solution which employs generalised functions to compute the dynamic properties of a damaged beam for a limited number of damage configurations; such a method avoids the enforcement of con-tinuity conditions at the cracked sections. Then, an explicit continuous expression of such dy-namic properties as a function of the damage intensities is proposed by employing the Sherman and Morrison formula. The proposed explicit approach is verified and applied for the evalua-tion of the dynamic properties of damaged beams; then, via modal superposition, the variability of the response associated to time histories is assessed as well as frequency-response curves for single and multi-cracked beams subjected to forced vibrations. |
