Interval Analysis of Dynamic Response of Structures

Abstract

In this paper, an interval method for the dynamic response of structures with uncertain parameters is proposed. The structural physical parameters and loads are considered as interval variables. The structural stiffness matrix, mass matrix and loading vectors are described as the sum of two parts corresponding to the deterministic matrix and the uncertainty of the interval parameters. The interval problem is then transformed into an approximate deterministic problem. The Laplace transform is used to convert the equations of the dynamic system into linear algebra equations. The effectiveness of the proposed method is demonstrated by a numerical example of a three-story structure. The results show that the range between upper and lower bounds of dynamic responses due to uncertain system parameters is narrow and acceptable. Since the presented method neglects the second order terms in the expansion of functions, the application of the approach is limited to the cases where the uncertainties of the parameters are small.