Interval Finite Element Approach for Modal Analysis of Linear Elastic Structures Under Uncertainty

We present a new Interval Finite Element (IFEM) approach for modal analysis of linear elastic structures with uncertain geometric and material properties. Uncertain parameters are modeled as intervals. Guaranteed interval lower and upper bounds for natural frequencies and modal shapes are attained using a new decomposition strategy of the IFEM matrices that drastically reduces overestimation due to interval dependency. The associated interval generalized eigenvalue problem is solved efficiently by way of a new variant of the iterative enclosure method. Several numerical examples show the accuracy and efficiency of the proposed method.