A Variational Formulation for Coupled Single-Walled Carbon Nanotubes Undergoing Vibrations in the Presence of an Axial Magnetic Field
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Bibliographic record
Abstract
A variational formulation is presented for a system consisting of two coupled singlewalled carbon nanotubes subjected to forced vibrations, longitudinal magnetic field, and axial compression, based on the nonlocal elasticity theory.The variational principle for the double nanotube system is derived, followed by the application of Hamilton's principle to express kinetic and potential energies.Subsequently, the time-independent scenario is investigated, and governing equations for the freely vibrating system are provided.The variational formulation for this case is established, and expressions for Rayleigh quotients concerning the vibration frequency and buckling load are derived.The Rayleigh quotient for the frequency demonstrates that the magnetic field increases the vibration frequency of the coupled nanotube system.Nonlocal effects appear in both the numerator and the denominator of the Rayleigh quotient, influencing the frequency increase or decrease depending on the relative values of various problem parameters.In contrast, the magnetic field reduces the buckling load, as evidenced by its negative contribution to the numerator of the Rayleigh quotient for buckling.The effect of the nonlocal parameter on buckling, however, cannot be inferred directly from the Rayleigh quotient.In this study, involving a system of two coupled partial differential equations, it is crucial to derive variationally consistent boundary conditions.Utilizing the formulated variational principle, variationally consistent natural boundary conditions are established in terms of moment and shear force expressions.It is revealed that the Pasternak interlayer between the nanotubes results in coupled boundary conditions when a shear force and/or a moment is specified at the boundaries of the nanotube system.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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