Natural frequencies and buckling of pressurized nanotubes using shear deformable nonlocal shell model

The small-scale effect on the natural frequencies and buckling of pressurized nanotubes is investigated in this study. Based on the firstorder shear deformable shell theory, the nonlocal theory of elasticity is used to account for the small-scale effect and the governing equations of motion are obta...

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Bibliographic Details
Published in:Journal of mechanical science and technology 2012, 26(2), , pp.563-573
Main Authors: Firouz-Abadi, R. D., Fotouhi, M. M., Permoon, M. R., Haddadpour, H.
Format: Article
Language:English
Subjects:
Buckling
Control
Dynamical Systems
Engineering
Exact sciences and technology
Formability
Fundamental areas of phenomenology (including applications)
Galerkin methods
Industrial and Production Engineering
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Mathematical models
Mechanical Engineering
Mechanical instruments, equipment and techniques
Micromechanical devices and systems
Nanostructure
Nanotubes
Physics
Resonant frequency
Shear
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Vibration
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:The small-scale effect on the natural frequencies and buckling of pressurized nanotubes is investigated in this study. Based on the firstorder shear deformable shell theory, the nonlocal theory of elasticity is used to account for the small-scale effect and the governing equations of motion are obtained. Applying modal analysis technique and based on Galerkin’s method a procedure is proposed to obtain natural frequencies of vibrations. For the case of nanotubes with simply supported boundary conditions, explicit expressions are obtained which establish the dependency of the natural frequencies and buckling loads of the nanotube on the small-scale parameter and natural frequencies obtained by local continuum mechanics. The obtained solutions generalize the results of nano-bar and -beam models and are verified by the literature. Based on several numerical studies some conclusions are drawn about the small-scale effect on the natural frequencies and buckling pressure of the nanotubes.
ISSN:1738-494X
1976-3824
DOI:10.1007/s12206-011-1039-y