Rayleigh–Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

2011 ◽  
Vol 375 (9) ◽  
pp. 1255-1263 ◽  
Author(s):  
R. Ansari ◽  
S. Sahmani ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Single Walled Carbon Nanotubes ◽  
Buckling Analysis ◽  
Different Boundary Conditions ◽  
Single Walled Carbon ◽  
Axial Buckling ◽  
Walled Carbon Nanotubes

Vibrational analysis of sandwich sectorial plates with functionally graded sheets reinforced by aggregated carbon nanotube

2018 ◽  
Vol 22 (5) ◽  
pp. 1496-1541 ◽  
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Single Walled Carbon Nanotubes ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Two Dimensional ◽  
Simply Supported ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded nanocomposite sandwich sectorial plates are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes are assumed to be graded in the thickness direction. To determine the effect of carbon nanotube agglomeration on the elastic properties of carbon nanotube-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby–Mori–Tanaka approach is considered to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight carbon nanotubes. The two-dimensional generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed sectorial plates are simply supported at radial edges, while all possible combinations of free, simply supported, and clamped boundary conditions are applied to the other two circular edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of agglomeration, geometrical, and material parameters together with the boundary conditions on the frequency parameters of the sandwich functionally graded nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of carbon nanotubes agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analyze the sandwich sectorial plates.

Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory

2019 ◽  
Vol 26 (11-12) ◽  
pp. 913-928 ◽  
Author(s):  
Seyed Amirhosein Hosseini ◽  
Farshad Khosravi ◽  
Majid Ghadiri
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Classical Theory ◽  
Moving Load ◽  
Nonlocal Parameter ◽  
Excitation Frequency ◽  
Single Walled Carbon Nanotubes ◽  
Axial Displacement ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

The main objective of the present work is devoted to the study of both free and time-dependent forced axial vibration simultaneously in single-walled carbon nanotubes subjected to a moving load. The governing equation is derived via Hamilton’s principle. Classical theory, along with the Rayleigh and Bishop theories, is used to analyze the nonlocal vibrational behaviors of single-walled carbon nanotubes. A Galerkin method is established to solve the derived equations. The boundary conditions are assumed to be clamped-clamped and clamped-free. Firstly, the variation of nondimensional natural frequencies is calculated based on the classical theory, and the effect of the nonlocal parameter, the mode number and the length is illustrated and schematically compared for clamped-clamped and clamped-free boundary conditions. Besides, the obtained nondimensional responses are compared with the results of another study to validate the accuracy of the used method. Ultimately, the dynamic axial displacement due to the moving load in the time domain has been studied for the first time. Furthermore, the effects of the thickness, length, velocity of the moving load, excitation frequency, and the nonlocal parameter based on the classical, Rayleigh, and Bishop theories are investigated in this paper. Also, the influence of the nonlocal parameter on the variations of maximum axial displacement with respect to the velocity parameter for the aforementioned boundary conditions and theories is evaluated relative to each other.

Analytical Treatment of the Free Vibration of Single-Walled Carbon Nanotubes Based on the Nonlocal Flugge Shell Theory

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Scale Effects ◽  
Elastic Shell ◽  
Nonlocal Parameter ◽  
Single Walled Carbon Nanotubes ◽  
Small Scale ◽  
Resonant Frequencies ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In the current work, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) under different boundary conditions are investigated. A nonlocal elastic shell model is utilized, which accounts for the small scale effects and encompasses its classical continuum counterpart as a particular case. The variational form of the Flugge type equations is constructed to which the analytical Rayleigh–Ritz method is applied. Comprehensive results are attained for the resonant frequencies of vibrating SWCNTs. The significance of the small size effects on the resonant frequencies of SWCNTs is shown to be dependent on the geometric parameters of nanotubes. The effectiveness of the present analytical solution is assessed by the molecular dynamics simulations as a benchmark of good accuracy. It is found that, in contrast to the chirality, the boundary conditions have a significant effect on the appropriate values of nonlocal parameter.

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