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Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation
This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mec...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9739529/ https://www.ncbi.nlm.nih.gov/pubmed/36500095 http://dx.doi.org/10.3390/ma15238599 |
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author | Herisanu, Nicolae Marinca, Bogdan Marinca, Vasile |
author_facet | Herisanu, Nicolae Marinca, Bogdan Marinca, Vasile |
author_sort | Herisanu, Nicolae |
collection | PubMed |
description | This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton’s principle, Eringen’s nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin–Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients. The nonlinear damped and forced vibration is studied using the optimal auxiliary functions method (OAFM). An explicit and very accurate analytical solution is obtained by means of OAFM without considering simplifying hypotheses. An accurate analysis is for the first time reported considering the cumulated effects of nonlinearities simultaneously induced by the Winkler–Pasternak foundation, the curvature of beams and van der Waals force, and also the effect of discontinuities marked by the presence of the Dirac function. Finally, a stability analysis of the considered model is developed by means of the homotopy perturbation method (HPM) using the condition of existence of the two frequencies. It was shown that an increasing of some constitutive parameters substantially reduces the area of stability, all these being of much help in guiding the design of advanced nanoelectromechanical devices, in which nanotubes act as basic elements. |
format | Online Article Text |
id | pubmed-9739529 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-97395292022-12-11 Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation Herisanu, Nicolae Marinca, Bogdan Marinca, Vasile Materials (Basel) Article This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton’s principle, Eringen’s nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin–Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients. The nonlinear damped and forced vibration is studied using the optimal auxiliary functions method (OAFM). An explicit and very accurate analytical solution is obtained by means of OAFM without considering simplifying hypotheses. An accurate analysis is for the first time reported considering the cumulated effects of nonlinearities simultaneously induced by the Winkler–Pasternak foundation, the curvature of beams and van der Waals force, and also the effect of discontinuities marked by the presence of the Dirac function. Finally, a stability analysis of the considered model is developed by means of the homotopy perturbation method (HPM) using the condition of existence of the two frequencies. It was shown that an increasing of some constitutive parameters substantially reduces the area of stability, all these being of much help in guiding the design of advanced nanoelectromechanical devices, in which nanotubes act as basic elements. MDPI 2022-12-02 /pmc/articles/PMC9739529/ /pubmed/36500095 http://dx.doi.org/10.3390/ma15238599 Text en © 2022 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 Herisanu, Nicolae Marinca, Bogdan Marinca, Vasile Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title | Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title_full | Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title_fullStr | Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title_full_unstemmed | Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title_short | Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation |
title_sort | nonlinear vibration of double-walled carbon nanotubes subjected to mechanical impact and embedded on winkler–pasternak foundation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9739529/ https://www.ncbi.nlm.nih.gov/pubmed/36500095 http://dx.doi.org/10.3390/ma15238599 |
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