Fuzzy variational principle for modal analysis of structures and its application

In this paper, the modal analysis to estimate eigenvalue and eigenvector of structures with fuzzy parameters is presented. By introducing fuzzy parameters into the Rayleigh quotient variation, the fuzzy variational principle is developed. The fuzzy finite element method is proposed as the application of the fuzzy variational principle. The proposed fuzzy finite element method can obtain fuzzy eigenvalues and fuzzy eigenvectors directly. However, when the conventional fuzzy finite element methods are used for fuzzy analysis, the fuzzy parameters have to be transformed into the interval parameters before the calculation and the fuzzy results are subsequently constructed by the interval results. The proposed method avoids these roundabout procedures in comparison with the conventional fuzzy finite element methods. Therefore, the proposed method can reduce the computational cost and increase computational efficiency. Numerical examples are presented to illustrate the validity and feasibility of the proposed method.