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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Estonian Academy Publishers
2025-05-01
|
| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | https://kirj.ee/wp-content/plugins/kirj/pub/proc-2-2025-234-239_20250516115001.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849328858359136256 |
|---|---|
| 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 |
| id | doaj-art-722dfa87c7a643a6a05378de1d7b261f |
| 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 |