Quantification of Uncertainties in Dynamic Structural Systems Using the Interval Analysis and the Finite Element Method
Fabiano Sangi de Oliveira1; José Juliano de Lima Junior1
1 Federal University of Itajubá
doi:10.20906/CPS/CILAMCE2017-0140
Resumo
Due to the great importance of quantifying the uncertainties present in mechanical systems, in this paper, we will present the problem of interval eigenvalue, with parametric uncertainties in the global mass matrices and rigidity of the system. Numerical examples will be presented, which will be solved through a computational method, using Interval Analysis, together with the Finite Element Method. To support the solution of the problem, the necessary fundamentals of Interval Arithmetic and the Finite Element Method will be presented. After solving the proposed problems, the eigenvalues and the natural frequencies of the system will be presented with Frequency Response graphs. For validation of the proposed method, numerical results and simulation graphs will be presented using the Monte Carlo Method.
Palavras-chave: Interval Analysis; Vibrating Systems; Eigenvalue Problem; Finite Elements