Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes
This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/3241698 |
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| author | Matteo Strozzi Francesco Pellicano |
| author_facet | Matteo Strozzi Francesco Pellicano |
| author_sort | Matteo Strozzi |
| collection | DOAJ |
| description | This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, and a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs are investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed. |
| format | Article |
| id | doaj-art-4988b173c4914eae8298e6f8dccfbd2f |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-4988b173c4914eae8298e6f8dccfbd2f2025-02-03T00:59:05ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/32416983241698Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon NanotubesMatteo Strozzi0Francesco Pellicano1Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Giovanni Amendola 2, 42122 Reggio Emilia, ItalyDepartment of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Via Pietro Vivarelli 10/1, 41125 Modena, ItalyThis paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, and a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs are investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.http://dx.doi.org/10.1155/2019/3241698 |
| spellingShingle | Matteo Strozzi Francesco Pellicano Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes Shock and Vibration |
| title | Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes |
| title_full | Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes |
| title_fullStr | Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes |
| title_full_unstemmed | Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes |
| title_short | Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes |
| title_sort | nonlinear resonance interaction between conjugate circumferential flexural modes in single walled carbon nanotubes |
| url | http://dx.doi.org/10.1155/2019/3241698 |
| work_keys_str_mv | AT matteostrozzi nonlinearresonanceinteractionbetweenconjugatecircumferentialflexuralmodesinsinglewalledcarbonnanotubes AT francescopellicano nonlinearresonanceinteractionbetweenconjugatecircumferentialflexuralmodesinsinglewalledcarbonnanotubes |