The time response of structures with bounded parameters and interval initial conditions

Uncertainty plays an important role in the performance of structures. In this paper, we focus on the dynamic response of structures with bounded parameters and interval initial conditions, and present a new method to determine the supremum and infimum of the time response. The method is based on the vertex solution theorem for the first-order deviation of the dynamic response from its central value and avoids interval extension problems present in current methods, where the length of the interval increases significantly due to the intermediate calculations. The method is more accurate than existing perturbation methods and provides tighter bounds on the response. The approach neglects the second-order terms in the equation of motion, and care should be exercised when the parameter variations are large. The other advantage of this method is its ability to solve problems with uncertainties in the initial conditions.