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Existence of second spectrums of Timoshenko beam and Mindlin–Herrmann rod theories on the basis of atomistic studies

Patra, AK and Gopalakrishnan, S and Ganguli, R (2020) Existence of second spectrums of Timoshenko beam and Mindlin–Herrmann rod theories on the basis of atomistic studies. In: Acta Mechanica, 231 (3). pp. 1159-1171.

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Official URL: https://doi.org/10.1007/s00707-019-02587-5


This paper considers a single-layer 2D triangular lattice system as an ideal higher-order rod and/or beam. The objective is to compare the solutions of these continuum models with the standard atomistic solutions. The accuracy of these higher-order rod and beam theories, in modeling several nano-systems, depends on the frequency of vibration. The existence of a second spectrum associated with these higher-order continuum theories and its contribution to the continuum solutions are studied on the basis of molecular dynamics (MD) results. It is shown that the second spectrum of a Timoshenko beam is less accurate with respect to the MD results but cannot be disregarded totally. Also, the existence of a second propagating mode associated with a Mindlin–Herrmann rod is substantiated by MD simulation results. The accuracy of these higher order rod and beam theories deteriorates beyond their cut-on frequencies. However, the use of higher-order rod and beam theories in several high-frequency dynamic and multiscale analyses is still justifiable

Item Type: Journal Article
Publication: Acta Mechanica
Publisher: Springer
Additional Information: The copyright for this article belongs to the Springer.
Keywords: Continuum mechanics; Molecular dynamics; Nanosystems, Atomistic studies; Continuum model; High frequency dynamics; Higher order continuum theories; Multi scale analysis; Propagating mode; Timoshenko beams; Triangular lattice, Particle beams
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 02 Feb 2023 05:13
Last Modified: 02 Feb 2023 05:13
URI: https://eprints.iisc.ac.in/id/eprint/79708

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