Dynamic Analysis of Structures with Uncertain-But-Bounded Parameters

Physical and geometrical uncertainties, which affect to a certain extent the structural response, are usually described following two contrasting points of view, known as probabilistic and nonprobabilistic approaches. The probabilistic approach is certainly the most widely adopted and can be developed by three main ways: the MCS method, the stochastic FE method [1] and the orthogonal series expansion method [2]. Unfortunately, these methods require a wealth of data, often unavailable, to define the probability distribution density of the uncertain structural parameters. In the framework of non-probabilistic approaches, today, the interval model may be considered as the most widely used analytical tool. This model is derived from the so-called Interval Analysis [3] in which the number is treated as an interval variable with lower and upper bounds. The main advantage of the interval analysis is that it provides rigorous enclosures of the solution, but its application to real engineering problems is quite difficult. In this paper, a novel procedure for the dynamic analysis of linear structural systems, with uncertain parameters, subjected to deterministic excitations is presented. Under the realistic assumption that available information is incomplete or fragmentary, the fluctuating properties are modeled as uncertain-but-bounded parameters via interval analysis. The proposed method requires the following steps: i) to split the response as sum of the midpoint solution and a deviation obtained by superimposing the deviations due to each uncertain parameter separately taken [4]; ii) to solve the sets of differential equations governing the midpoint and deviation vectors; iii) to evaluate the lower and upper bounds of the structural response by handy formulas. The effectiveness of the presented procedure is demonstrated by numerical results included in the paper.