Abstract
The model of single-walled carbon nanotubes nonlinear vibrations, which is based on shell theory, is derived. The system of partial differential equations with respect to three displacements projections is obtained using the Sanders–Koiter shell theory and nonlocal elasticity. The system of nonlinear ordinary differential equations, which describes the nanotubes vibrations, is obtained by the Galerkin method. The harmonic balanced method is used to calculate free nonlinear vibrations. The bifurcation behavior of CNT vibrations owing to the Naimark–Sacker bifurcation is analyzed. Almost periodic vibrations of carbon nanotubes are investigated numerically. The nanotube periodic and almost periodic vibrations have three displacements projections u,v,w, which are commensurable. This is essential difference of the nanotube vibrations from macroshells.
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