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Acta Mechanica

Erschienen in:

18.12.2019 | Original Paper

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

verfasst von: Amit K. Patra, S. Gopalakrishnan, Ranjan Ganguli

Erschienen in: Acta Mechanica | Ausgabe 3/2020

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Abstract

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.

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Titel: Existence of second spectrums of Timoshenko beam and Mindlin–Herrmann rod theories on the basis of atomistic studies
verfasst von: Amit K. Patra
S. Gopalakrishnan
Ranjan Ganguli
Publikationsdatum: 18.12.2019
Verlag: Springer Vienna
Erschienen in: Acta Mechanica / Ausgabe 3/2020
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-019-02587-5

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