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Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model

Dynamic stability is an important mechanical behavior of nanobeams, which has been studied extensively using the Euler–Bernoulli and Timoshenko beam theories, while the Levinson-beam-theory-based dynamic instability analysis of nanobeams has not been investigated yet. Shear deformation is not or is...

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Autores principales: Huang, Youqin, Huang, Richeng, Huang, Yonghui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10180475/
https://www.ncbi.nlm.nih.gov/pubmed/37176285
http://dx.doi.org/10.3390/ma16093404
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author Huang, Youqin
Huang, Richeng
Huang, Yonghui
author_facet Huang, Youqin
Huang, Richeng
Huang, Yonghui
author_sort Huang, Youqin
collection PubMed
description Dynamic stability is an important mechanical behavior of nanobeams, which has been studied extensively using the Euler–Bernoulli and Timoshenko beam theories, while the Levinson-beam-theory-based dynamic instability analysis of nanobeams has not been investigated yet. Shear deformation is not or is not suitably considered in the Euler–Bernoulli and Timoshenko theories, so it is very important to introduce the Levinson beam theory in the dynamic stability analysis of nanobeams, which correctly models the combined action of bending and shear in nanobeams with smaller length/height ratios. In this work, the equation of the transverse vibration of a Levinson beam embedded in an elastic foundation is firstly formulated based on the displacement field of Levinson beam theory, and the nonlocal theory is further applied to the Levinson nanobeam. Then, the governing equation of the dynamic stability of the Levinson nanobeam is derived using Bolotin’s method to achieve a generalized eigenvalue problem corresponding to the boundaries of regions of dynamic instability. The principal instability region (PIR) is the most important among all regions, so the boundary of the PIR is focused on in this work to investigate the dynamic stability of the Levinson nanobeam. When the width, length/height ratio, density, Young’s modulus, Poisson’s ratio, size scale parameter, and medium stiffness increase by about 1.5 times, the width of the PIR changes by about 19%, −57%, −20%, 65%, 0, −9%, and −11%, respectively. If a smaller critical excitation frequency and narrower width of the PIR correspond to the better performance of dynamic stability, the study shows that the dynamic stability of the Levinson nanobeam embedded in an elastic medium improves under a larger length and density and a smaller width, height, and Young’s modulus, since these factors are related to the natural frequency of the nanobeam which controls the width of the PIR. Additionally, the local model would overestimate the dynamic stability behavior of the Levinson nanobeam.
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spelling pubmed-101804752023-05-13 Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model Huang, Youqin Huang, Richeng Huang, Yonghui Materials (Basel) Article Dynamic stability is an important mechanical behavior of nanobeams, which has been studied extensively using the Euler–Bernoulli and Timoshenko beam theories, while the Levinson-beam-theory-based dynamic instability analysis of nanobeams has not been investigated yet. Shear deformation is not or is not suitably considered in the Euler–Bernoulli and Timoshenko theories, so it is very important to introduce the Levinson beam theory in the dynamic stability analysis of nanobeams, which correctly models the combined action of bending and shear in nanobeams with smaller length/height ratios. In this work, the equation of the transverse vibration of a Levinson beam embedded in an elastic foundation is firstly formulated based on the displacement field of Levinson beam theory, and the nonlocal theory is further applied to the Levinson nanobeam. Then, the governing equation of the dynamic stability of the Levinson nanobeam is derived using Bolotin’s method to achieve a generalized eigenvalue problem corresponding to the boundaries of regions of dynamic instability. The principal instability region (PIR) is the most important among all regions, so the boundary of the PIR is focused on in this work to investigate the dynamic stability of the Levinson nanobeam. When the width, length/height ratio, density, Young’s modulus, Poisson’s ratio, size scale parameter, and medium stiffness increase by about 1.5 times, the width of the PIR changes by about 19%, −57%, −20%, 65%, 0, −9%, and −11%, respectively. If a smaller critical excitation frequency and narrower width of the PIR correspond to the better performance of dynamic stability, the study shows that the dynamic stability of the Levinson nanobeam embedded in an elastic medium improves under a larger length and density and a smaller width, height, and Young’s modulus, since these factors are related to the natural frequency of the nanobeam which controls the width of the PIR. Additionally, the local model would overestimate the dynamic stability behavior of the Levinson nanobeam. MDPI 2023-04-26 /pmc/articles/PMC10180475/ /pubmed/37176285 http://dx.doi.org/10.3390/ma16093404 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Huang, Youqin
Huang, Richeng
Huang, Yonghui
Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title_full Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title_fullStr Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title_full_unstemmed Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title_short Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
title_sort investigation into the dynamic stability of nanobeams by using the levinson beam model
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10180475/
https://www.ncbi.nlm.nih.gov/pubmed/37176285
http://dx.doi.org/10.3390/ma16093404
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AT huangricheng investigationintothedynamicstabilityofnanobeamsbyusingthelevinsonbeammodel
AT huangyonghui investigationintothedynamicstabilityofnanobeamsbyusingthelevinsonbeammodel