Article

Received 21.02.2024

Revised 22.05.2024

Accepted 29.06.2024

Retrieved from Vol. 28, No. 1 2024

Pages 203 -211

Shlyun, N. (2024). Flat and spatial periodic bending oscillations of elongated carbon nanotubes. The National Transport University Bulletin, 28(1), 203-211. https://doi.org/10.33744/2308-6645-2024-1-58-203-211

Flat and spatial periodic bending oscillations of elongated carbon nanotubes

Nataliia Shlyun

The processes of planar and spatial periodic bending vibration in elongated carbon nanotubes prestressed by axial forces and torques have been investigated. With the use of effective parameters of geometry and mechanics, differential equations of their elastic transverse dynamics for the considered prestresses are constructed. It is shown, that in the first case, the free vibrations of the nanotube are described by a fourth order differential equation, in the second case – the order of the equation order enlarges to eight. The solutions of these equations are built in closed form. It is established that if the nanotube is prestressed only by a longitudinal force, then its free periodic motions can be realized only in the form of planar standing and running harmonic waves. When it is prestressed by a torque, the modes of its vibrations are standing or running, left and right circular cylindrical helixes. Topicality of the performed investigation is associated with very high mechanical properties of the carbon nanotubes and low level of their investigation

carbon nanotubes; prestressed state; differential equations; elastic oscillations; plane waves; spiral waves
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https://doi.org/10.33744/2308-6645-2024-1-58-203-211