This paper aims to study the uncertainty of the MDOF structural dynamic response, taking not only the interval characteristics of structural physical parameters and geometric dimension, but also the interval characteristics of applied load simultaneously . By means of the description of the interval parameters of uncertain structure with affine forms, the interval structural dynamic equation is studied, and an improved affine arithmetic based on interval division is presented, where correlations between the interval elements in eigenvalue and responses equations are considered, independent uncertain parameters are transformed to affine forms, and the solution of eigenvalue and response equations are transformed into the corresponding certain ones. With general affine arithmetic, the eigenvalue of each order and response bounds are determined by searching for the maximum and minimum in the solutions. Finally, some mathematical examples and a further engineering application confirm the feasibility and validity of this approach.

By representing the uncertain parameters as interval numbers, the reliability index equations of bars structures were obtained. A modified matrix affine arithmetic polynomial evaluation method plus recursive derivative information was proposed in this paper, which keeps all powers of noise symbols without approximation. Based on the nature that affine forms and intervals variables could transform each other, affine forms of bounded uncertain variables and modified affine arithmetic including derivative information for interval univariate polynomial evaluation were introduced into modeling and calculating non-probabilistic reliability index. An extended beam example and a ten-bar truss structure example were provided to illustrate the validity and feasibility of the presented procedures.