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-bounded parameters subjected to deterministic dynamic loads. A novel procedure based on the use of sensitivity analysis in conjunction with classical modal superposition method is proposed. Specifically, a pseudo-static sensitivity analysis is performed to seek the combinations of the endpoints of the uncertain parameters which give the lower bound and upper bound of the response at each time instant. Among these, two combinations are selected as the most common ones over the time interval of interest in order to avoid the onerous updating of the uncertain parameters at each time instant. Then, the bounds of the response time-history are evaluated by performing two parallel deterministic modal analyses associated to the most common combinations of the extreme values of interval uncertainties. Numerical results demonstrate that the proposed method is more efficient than both the Interval Perturbation Method (IPM) and the classical combinatorial procedure. Furthermore, unlike the IPM, it allows the analysis of large-size structures exhibiting relatively large fluctuations of the uncertain parameters.