Dynamic analysis of multi-cracked truss and frame structures with uncertain-but-bounded damage

The present paper aims to provide a contribution in the study of the dynamic response of cracked truss-like and frame-like structures with uncertain damage modeled by following a non-probabilistic approach. By adopting a finite element model to describe the cracked members with fully open cracks, in the framework of the interval analysis, the parameters identifying the cracks depths are modeled as uncertain‑but-bounded variables. The proposed procedure allows to evaluate lower and upper bounds of the time-varying response of multi-cracked trusses and frames subjected to deterministic excitation by applying two parallel generalized modal analyses corresponding to two appropriate combinations of the endpoints of the interval uncertainties. The method is validated through numerical tests and its accuracy is confirmed by the excellent agreement between the response bounds calculated via the present approach compared with the exact reference bounds derived by a combinatorial procedure (vertex method) merged with the Monte Carlo method.