Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates

2011 ◽  
Vol 93 (7) ◽  
pp. 1631-1639 ◽  
Author(s):  
P. Malekzadeh ◽  
A.R. Setoodeh ◽  
A. Alibeygi Beni
Keyword(s):  
Free Vibration ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

Energy meaning of small-scale effect on free vibration of carbon nanotubes

2014 ◽  
Vol 10 (5/6) ◽  
pp. 415
Author(s):  
Li Ming ◽  
Zheng Huiming ◽  
Luo Xia ◽  
Liu Yang
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

SMALL SCALE EFFECT ON THE FREE VIBRATION OF MULTI-WALLED CARBON NANOTUBES

2008 ◽  
Vol 22 (28) ◽  
pp. 2769-2777 ◽  
Author(s):  
Y. YAN ◽  
W. Q. WANG ◽  
L. X. ZHANG
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Scale Effect ◽  
Large Scale ◽  
Small Scale ◽  
Beam Model ◽  
Aspect Ratios ◽  
Small Scale Effect ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper is concerned with the free vibration of multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on the non-local elasticity theory, Timoshenko beam model with the small scale effect and the van der Waals (vdW) interaction is derived and then solved analytically. The results reveal that the small scale effect is quite significant for small aspect ratios, large scale parameters and high radial vibration modes, whereas it is insensitive to the number of layers of MWCNTs and is weakly-dependent on the wall thickness of MWCNTs.

A Theoretical Approach for Free Vibration Analysis of the Nano-Plates Considering the Small Scale Effect

2010 ◽  
Author(s):  
Emad Jomehzadeh ◽  
Ali Reza Saidi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Small Scale ◽  
Edge Zone ◽  
Wide Range ◽  
Small Scale Effect

The free vibration analysis of a nano-plate is investigated based on the first order shear deformation theory considering the small scale effect. The governing equations of motion are obtained using Hamilton’s principle by considering the nonlocal constitutive equations of Eringen. These coupled partial differential equations are reformulated into two new equations called the edge-zone and interior equations. Analytical solutions are obtained for a nano-plate with Levy boundary conditions. In order to find the natural frequencies of the nano-plate, the various boundary conditions at one direction of the plate should be imposed. Applying these conditions and setting the determinant of the six order coefficient matrix equal to zero, the natural frequencies of the nano-plate are evaluated. Non-dimensional frequency parameters are presented for over a wide range of nonlocal parameters and different boundary conditions. In addition, the effects of nonlocal parameter on the natural frequency of a nano-plate are discussed in details.

Small-scale effect on the mechanical properties of metallic nanotubes

2012 ◽  
Vol 101 (9) ◽  
pp. 093109 ◽  
Author(s):  
Jin Zhang ◽  
Chengyuan Wang ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Mechanical Properties ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect
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