Dynamic response bound analysis for elastic beams under uncertain excitations

Abstract

By introducing the interval process model, a non-random vibration analysis method is proposed in this paper to calculate the dynamic displacement response bounds of elastic beams under uncertain excitations. Firstly, based on the interval process model, a conception of spatial-time interval field is proposed to describe the uncertainty of excitations in spatial and time domain. Secondly, the middle point function and the radius function of displacement response of the elastic beam are deduced by combining the spatial-time interval field and the traditional mode superposition method, based on which an analytical formulation of the upper and lower displacement response bound functions of the elastic beam are obtained. In addition, the displacement response bound functions of a simply supported beam structure under two types of external excitations, namely the concentrated load and the sinusoidal distributed load, are given. Finally, several numerical examples are investigated to demonstrate the effectiveness of the proposed method.