In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.
Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response
Manuscript received June 21, 2016; final manuscript received May 10, 2017; published online June 12, 2017. Assoc. Editor: Mario Di Paola.
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Autuori, G., Cluni, F., Gusella, V., and Pucci, P. (June 12, 2017). "Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response." ASME. ASME J. Risk Uncertainty Part B. September 2017; 3(3): 030902. https://doi.org/10.1115/1.4036806
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