Sumelka, W.Zaera, RamónFernández-Sáez, José2022-12-132022-12-132015-09-01Sumelka, W., Zaera, R., & Fernández-Sáez, J. (2015). A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics. Meccanica, 50(9), 2309–2323.0025-64551572-9648 (electronic)https://hdl.handle.net/10016/36170In this paper we present a theoretical analysis of free axial vibrations of rods described in terms of the fractional continuum mechanics. This formulation is able to capture the size effect arising in different problems of solid mechanics. The natural frequencies and modal shapes for clamped rods are obtained and the effects of the derivative order, as well as the corresponding length-scale parameters in the fractional model are discussed. The results are compared with those derived from the Eringen non-local elasticity theory, which is an approach widely used to model structures showing size effects.15eng© The Author(s) 2015. This article is published with open access at Springerlink.comThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Atribución 3.0 EspañaNon-local modelsRodsFractional calculusresearch articleIngeniería Mecánicahttps://doi.org/10.1007/s11012-015-0157-5open access230992323Meccanica50AR/0000017148