Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes

Longitudinal wave propagation in axially functionally graded carbon nanotubes was investigated using three different solution methods: analytical, higher order Haar wavelet and Ritz methods. The results of the various solution methods were compared and validated. A weak form solution for the wave fr...

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Main Authors: Mustafa Arda, Tamer Tosun
Format: Article
Language:English
Published: Estonian Academy Publishers 2025-05-01
Series:Proceedings of the Estonian Academy of Sciences
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Online Access:https://kirj.ee/wp-content/plugins/kirj/pub/proc-2-2025-234-239_20250516115001.pdf
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author Mustafa Arda
Tamer Tosun
author_facet Mustafa Arda
Tamer Tosun
author_sort Mustafa Arda
collection DOAJ
description Longitudinal wave propagation in axially functionally graded carbon nanotubes was investigated using three different solution methods: analytical, higher order Haar wavelet and Ritz methods. The results of the various solution methods were compared and validated. A weak form solution for the wave frequency was presented using the Lagrangian energy functional and the Ritz method. Exponential and power-law material grading variations were considered. Material grading parameters and grading nonlocality effects on the axial wave propagation frequency were investigated. The present study could be useful in the wave dynamic analysis of axially graded nanostructures.
format Article
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institution Kabale University
issn 1736-6046
1736-7530
language English
publishDate 2025-05-01
publisher Estonian Academy Publishers
record_format Article
series Proceedings of the Estonian Academy of Sciences
spelling doaj-art-722dfa87c7a643a6a05378de1d7b261f2025-08-20T03:47:25ZengEstonian Academy PublishersProceedings of the Estonian Academy of Sciences1736-60461736-75302025-05-01742234239https://doi.org/10.3176/proc.2025.2.27https://doi.org/10.3176/proc.2025.2.27Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubesMustafa Arda0Tamer Tosun1Department of Mechanical Engineering, Trakya University, Edirne, TurkeyInstitute of Natural and Applied Sciences, Trakya University, Edirne, TurkeyLongitudinal wave propagation in axially functionally graded carbon nanotubes was investigated using three different solution methods: analytical, higher order Haar wavelet and Ritz methods. The results of the various solution methods were compared and validated. A weak form solution for the wave frequency was presented using the Lagrangian energy functional and the Ritz method. Exponential and power-law material grading variations were considered. Material grading parameters and grading nonlocality effects on the axial wave propagation frequency were investigated. The present study could be useful in the wave dynamic analysis of axially graded nanostructures.https://kirj.ee/wp-content/plugins/kirj/pub/proc-2-2025-234-239_20250516115001.pdfaxially gradedlongitudinalwave propagationcarbon nanotubesnonlocal elasticity
spellingShingle Mustafa Arda
Tamer Tosun
Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
Proceedings of the Estonian Academy of Sciences
axially graded
longitudinal
wave propagation
carbon nanotubes
nonlocal elasticity
title Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
title_full Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
title_fullStr Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
title_full_unstemmed Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
title_short Ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
title_sort ritz formulation for the wave propagation analysis of axially functionally graded carbon nanotubes
topic axially graded
longitudinal
wave propagation
carbon nanotubes
nonlocal elasticity
url https://kirj.ee/wp-content/plugins/kirj/pub/proc-2-2025-234-239_20250516115001.pdf
work_keys_str_mv AT mustafaarda ritzformulationforthewavepropagationanalysisofaxiallyfunctionallygradedcarbonnanotubes
AT tamertosun ritzformulationforthewavepropagationanalysisofaxiallyfunctionallygradedcarbonnanotubes