INVESTIGATION OF SIZE EFFECTS ON STATIC RESPONSE OF SINGLE-WALLED CARBON NANOTUBES BASED ON STRAIN GRADIENT ELASTICITY

2012 ◽  
Vol 09 (02) ◽  
pp. 1240032 ◽  
Author(s):  
B. AKGÖZ ◽  
Ö. CİVALEK
Keyword(s):  
Carbon Nanotubes ◽  
Strain Gradient ◽  
Couple Stress ◽  
Gradient Elasticity ◽  
Single Walled Carbon Nanotubes ◽  
Stress And Strain ◽  
Strain Gradient Elasticity ◽  
Single Walled Carbon ◽  
Modified Couple Stress ◽  
Walled Carbon Nanotubes

This paper is concerned with the bending analysis of single-walled carbon nanotubes (CNT) based on modified couple stress and strain gradient elasticity theories and Euler–Bernoulli beam theory. The size effect is taken into consideration using the modified couple stress and strain gradient elasticity theories. The governing equations and boundary conditions are derived using the variational approach. Deflections of CNT are obtained and presented in graphical form. Results are presented to show the effect of small-scale effect on bending of CNT. It is the first time in the literature, analytical expression and their solutions for the bending analysis based on strain gradient elasticity and couple stress theories are given for CNT under uniformly distributed load and concentrated end load.

scholarly journals Small size and rotary inertia effects on the natural frequencies of carbon nanotubes

2018 ◽  
Vol 5 (1) ◽  
pp. 273-279 ◽  
Author(s):  
Ömer Civalek ◽  
Hakan Ersoy ◽  
Hayri Metin Numanoğlu ◽  
Bekir Akgöz
Keyword(s):  
Carbon Nanotubes ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Single Walled Carbon Nanotubes ◽  
Rotary Inertia ◽  
Solution Technique ◽  
Single Walled Carbon ◽  
Rayleigh Beam ◽  
Modified Couple Stress ◽  
Walled Carbon Nanotubes

AbstractIn the present paper, rotary inertia and small size effects on the free vibration response of single-walled carbon nanotubes are examined. The equations in motion and associated boundary conditions are obtained by using Hamilton’s principle on the basis of modified couple stress and Rayleigh beam theories. The size effect is taken into account by modified couple stress theory while the rotary inertia effect is considered by Rayleigh beam theory. The resulting equations are analytically solved by implementing Navier’s solution technique for pinned-pinned carbon nanotubes. Influences of slenderness ratio, length scale parameter and rotary inertia on the natural frequencies of single-walled carbon nanotubes are studied in detail.

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