Dynamic analysis of Bernoulli-Euler beams with interval uncertainties under moving loads

This paper deals with the dynamic analysis of Bernoulli-Euler beams with uncertain parameters crossed by moving loads. Uncertainties associated with mass density, Young's modulus and load velocity are modeled as interval variables with given lower bounds and upper bounds. In order to evaluate the bounds of the interval displacement of the beam, an efficient procedure based on the use of the classical modal superposition method in conjunction with the improved interval analysis via extra unitary interval is developed. The key idea is to seek the bounds of the response by exploring just a few combinations of the endpoints of the uncertain parameters appropriately selected based on those yielding the minimum and maximum values of the interval natural frequencies.