Uncertain Response Analysis of Fractionally-Damped Beams Based on Interval Process Model

In the uncertain vibration analysis of fractionally-damped beams whose damping characteristic is described using fractional derivative model, the uncertain excitation is usually modeled as a stochastic process. However, it is often difficult to obtain sufficient samples of the excitation to establish a precise probability distribution function for the stochastic process model in practical engineering problems. Hence, in this paper, a nonrandom vibration analysis method for fractionally-damped beams is proposed to obtain the dynamic displacement response bounds of the beams under the uncertain excitation. Specifically, the uncertain excitation applied to the fractionally-damped beam is treated as a spatial-time interval field, so that the dynamic displacement response of the beam is also a space-time interval field. The middle point function and the radius function of the displacement response of the fractionally-damped beam can be derived based on the modal superposition method and the Laplace transform, through which the bound functions of the dynamic displacement response can be obtained. In addition, several numerical examples are given to demonstrate the effectiveness of the proposed method.