Dynamics of structures with uncertain-but-bounded parameters via pseudo-static sensitivity analysis

This paper deals with the analysis of linear-elastic structures with uncertain-but-boundedparameters subjected to deterministic dynamic loads. A novel procedure based on the useof sensitivity analysis in conjunction with classical modal superposition method is proposed.Specifically, a pseudo-static sensitivity analysis is performed to seek the combinationsof the endpoints of the uncertain parameters which give the lower bound and upperbound of the response at each time instant. Among these, two combinations are selectedas the most common ones over the time interval of interest in order to avoid the onerousupdating of the uncertain parameters at each time instant. Then, the bounds of theresponse time-history are evaluated by performing two parallel deterministic modal analysesassociated to the most common combinations of the extreme values of interval uncertainties.Numerical results demonstrate that the proposed method is more efficient than both theInterval Perturbation Method (IPM) and the classical combinatorial procedure. Furthermore,unlike the IPM, it allows the analysis of large-size structures exhibiting relatively large fluctuationsof the uncertain parameters.