Gómez Silva, FranciscoFernández-Sáez, JoséZaera, Ramón2022-12-132022-12-132022-03-01Gómez-Silva, F., Fernández-Sáez, J., & Zaera, R. (2022). Nonstandard continualization of 1D lattice with next-nearest interactions. Low order ODEs and enhanced prediction of the dispersive behavior. Mechanics of Advanced Materials and Structures, 29(6), 923–932.1537-64941537-6532 (online)https://hdl.handle.net/10016/36172In this article, different standard and nonstandard continualization techniques are applied to a one-dimensional solid consisting in a chain of masses interacting with nearest and next-nearest neighbors through linear springs. The study focuses on the reliability of the different continua in capturing the dispersive behavior of the discrete, on the order of the continuous governing equation because of its effect on the need for including nonclassical boundary conditions, as well as on the physical inconsistencies that appear for short wavelengths. The Regularization method, used by Bacigalupo and Gambarotta for a lattice with nearest interactions, presents advantages over the others.10eng© 2020 The Author(s). Published with license by Taylor and Francis Group, LLCThis is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.Atribución-NoComercial-SinDerivadas 3.0 EspañaNext-nearest interactionsLattice dynamicsDispersive behaviorContinualizationShift operatorRegularizationresearch articleIngeniería Mecánicahttps://doi.org/10.1080/15376494.2020.1799271open access9236932Mechanics of Advanced Materials and Structures29AR/0000029658