On estimating frequency response function envelopes using the spectral element method and fuzzy sets

The influence of uncertain input data on response spectra of dynamic structures is considered. Traditionally, frequency response analyses are based on finite or boundary element models of the objective structure. In the case of the mid-frequency range problem, however, a very fine mesh is required to correctly approximate the frequency response. This is particularly problematic in uncertainty modeling where the computational effort is usually increased significantly by the need for multiple runs (e.g. when conducting a Monte Carlo analysis) to achieve reliable results. In this paper, the spectral element method, combined with a fuzzy set-based uncertainty modeling approach, is presented as an appealing alternative, provided that the models are simple enough to yield a spectral element representation. To conduct the fuzzy analysis part, three different implementations of the extension principle of fuzzy arithmetic are applied and compared. The suitability of each method depends on the number of uncertain parameters, the problem characteristics, and the required accuracy of the results. The performance of the proposed approach is illustrated by two test problems, a simple coupled rod and a reinforced plate model. To verify the fuzzy-valued results, a Monte Carlo simulation has also been included. (c) 2005 Elsevier Ltd. All rights reserved.