Effects of shear deformation on vibration of doublewalled carbon nanotubes embedded in an elastic medium |
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Authors: | Metin Aydogdu |
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Institution: | (1) Department of Mechanical Engineering, Engineering and Architecture Faculty, Trakya University, Edirne, Turkey |
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Abstract: | In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) embedded in an elastic medium was investigated
by using the generalized shear deformation-beam theory (GSDBT). The effects of surrounding elastic medium, which is considered
as a spring, defined by the Winkler model, and van der Waals forces from adjacent nanotubes are taken into account. Third-order
shear deformation (TOSD) theory is used to study free vibration of a multi-walled carbon nanotube embedded in an elastic medium.
Unlike Timoshenko beam theory, TOSD theory satisfies zero traction boundary conditions on the upper and lower surface of the
structures, so there is no need to use a shear correction factor. Free vibration frequencies and amplitude ratios were obtained
for various sides to thickness ratios and elastic medium effects and results are compared with previous studies. The results
showed that significant difference exist between TOSD and Euler beam theory. It is also interesting to note that, although
frequency parameter is increasing by increasing stiffness of embedded medium, amplitude ratios are insensitive to stiffness
of embedded elastic medium.
Dedicated to the honorable memory of my beloved mother Fatma Aydogdu (Romania,1933-Tekirdag, August 7, 2007) |
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Keywords: | Nano-structures Vibration Multi-walled carbon nanotubes Third-order shear deformation theory |
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