Fuzzy-Affine Approach in Dynamic Analysis of Uncertain Structural Systems

Abstract

AbstractThe dynamic analysis of a structural system with different material and geometric properties leads to linear eigenvalue problem such as generalized (or standard) eigenvalue problem. In general, the material and geometric properties are assumed to be in the form of crisp (or exact). However, due to several errors and insufficient or incomplete information of data, the uncertainties are assumed to be present in the material and geometric properties. These uncertain material and geometric properties may be modeled through convex normalized fuzzy sets. In standard fuzzy arithmetic, all the operands are assumed to be independent of each other. But when they are partially or completely dependent on each other, the standard fuzzy arithmetic results in a wider range. This situation is known as the “dependency problem” or “overestimation problem”. In this regard, a fuzzy-affine approach is developed to overcome the dependency problem. This proposed approach may improve the outer enclosures and give tighter bounds to the fuzzy solution set. This chapter deals with the dynamic analysis of various structural systems viz. multi degrees-of-freedom spring-mass structural system, multi-storey frame structural system, etc. by adopting the proposed approach. Several numerical examples related to the dynamic analysis of these structural systems have been worked out to illustrate the reliability and efficiency of the present approach.KeywordsAffine arithmeticFuzzy-affine arithmeticDynamic analysis of structural systemFuzzy generalized eigenvalue problemFuzzy standard eigenvalue problem