Interval dynamic response of discretized structures with uncertain-but-bounded parameters

The dynamic analysis of structures plays an important role in the design of structural systems. Unfortunately, mechanical properties are usually uncertain due to physical imperfections and model inaccuracies. Therefore, it is important to estimate the effects of these uncertainties on the structural dynamic response. Since information regarding structural parameters is often quite limited, the use of non-probabilistic approaches is deemed advisable to realistically characterize uncertainties. In the framework of these approaches, the interval method seems today the most widely adopted. The interval dynamic analysis of structures with slight parameter fluctuations is usually performed by applying the Interval Perturbation Method (IPM). However, the effectiveness of the IPM is limited to small uncertainties since the effect of neglecting higher-order terms is unpredictable. In this paper, a novel procedure, able to overcome the main limitations of the IPM is proposed for evaluating the lower and upper bounds of the response of linear structural systems, with uncertain-but-bounded properties, subjected to dynamic deterministic excitations. The accuracy of the proposed method is assessed by evaluating the bounds of the response of a truss structure and a shear type frame subjected to seismic acceleration.