Vibration of Double-Walled Carbon Nanotube-Based Mass Sensor via Nonlocal Timoshenko Beam Theory

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhi-Bin Shen ◽  
Bin Deng ◽  
Xian-Fang Li ◽  
Guo-Jin Tang
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Tube Length ◽  
Beam Model ◽  
Mass Sensor ◽  
Nonlocal Timoshenko Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Tip Mass

The potential of double-walled carbon nanotubes (DWCNTs) as a micromass sensor is explored. A nonlocal Timoshenko beam carrying a micromass at the free end of the inner tube is used to analyze the vibration of DWCNT-based mass sensor. The length of the outer tube is not equal to that of the inner tube, and the interaction between two tubes is governed by van der Waals force (vdW). Using the transfer function method, the natural frequencies of a nonlocal cantilever with a tip mass are computed. The effects of the attached mass and the outer-to-inner tube length ratio on the natural frequencies are discussed. When the nonlocal parameter is neglected, the frequencies reduce to the classical results, in agreement with those using the finite element method. The obtained results show that increasing the attached micromass decreases the natural frequency but increases frequency shift. The mass sensitivity improves for short DWCNTs used in mass sensor. The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short DWCNT sensors. Obtained results are helpful to the design of DWCNT-based resonator as micromass sensor.

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

2021 ◽  
pp. 108128652110312
Author(s):  
Hooman Danesh ◽  
Mahdi Javanbakht
Keyword(s):  
Free Vibration ◽  
Elasticity Theory ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Two Phase ◽  
Softening Effect

Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. However, due to the different nonlocal averaging processes, they are expected to yield different results in their nonlocal forms. In the present work, the free vibration behavior of nonlocal nanobeams is studied using the nonlocal integral Timoshenko beam theory (NITBT) and two-dimensional nonlocal integral elasticity theory (2D-NIET) with different kernels and their results are compared. A new kernel, termed the compensated two-phase (CTP) kernel, is introduced, which entirely compensates for the boundary effects and does not suffer from the ill-posedness of previous kernels. Using the finite element method, the free vibration analysis is performed for different boundary conditions based on the first three natural frequencies. For both the NITBT and 2D-NIET with both the two-phase (TP) and CTP kernels, the nonlocal parameter has a softening effect on the natural frequencies for all the boundary conditions, without observing the paradoxical behaviors of the nonlocal differential theory. For both theories, the softening effect of the nonlocal parameter is more pronounced for the TP kernel compared to the CTP kernel. The sensitivity of the 2D-NIET to the nonlocal parameter is found to be higher than that of the NITBT. Also, the softening effects for different vibration modes are compared to each other for both theories and both kernels. The obtained results can be extended for various important beam problems with nonlocal effects and help obtain a better understanding of applicable nonlocal theories.

scholarly journals Influence of the nonlocal parameter on the transverse vibration of double-walled carbon nanotubes

2015 ◽  
Vol 24 (3-4) ◽  
pp. 79-90
Author(s):  
Fernanda de Borbón ◽  
Daniel Ambrosini
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Elastic Stiffness ◽  
Beam Model ◽  
Transverse Vibrations ◽  
Proposed Model ◽  
Cubic Polynomials ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractA high-order nonlocal continuum beam model is proposed, which can be applied to study the transverse vibrations of double-walled carbon nanotubes (DWCNTs), including those that could have initial deformations due to defects or external actions. A beam element is developed adopting Hermite cubic polynomials as shape functions, and mass and elastic stiffness matrix are presented. The influence of the nonlocal parameter on the vibrational properties of DWCNTs is studied. Using the proposed model, it was found that the nonlocal parameter has a strong influence on the natural frequencies.

Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values

2019 ◽  
Vol 19 (04) ◽  
pp. 1950036 ◽  
Author(s):  
Erol Demirkan ◽  
Reha Artan
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Small Scale ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Initial Values ◽  
Nonlocal Timoshenko Beam Theory ◽  
Small Scale Effect ◽  
Carry Over ◽  
Euler Bernoulli Beam

Investigated herein is the buckling of nanobeams based on a nonlocal Timoshenko beam model by the method of initial values within the framework of nonlocal elasticity. Since the nonlocal Timoshenko beam theory is of higher order than the nonlocal Euler–Bernoulli beam theory, it is known to be superior in predicting the small-scale effect. The buckling determinants and critical loads for bars with various kinds of supports are presented. The Carry-Over matrix (Transverse Matrix) is presented and the priorities of the method of initial values are depicted. To the best of the researchers’ knowledge, this is the first work that investigates the buckling of nonlocal Timoshenko beam with the method of initial values.

scholarly journals Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Suihan Sui ◽  
Ling Chen ◽  
Cheng Li ◽  
Xinpei Liu
Keyword(s):  
Power Law ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Vibration Modes ◽  
Graded Materials ◽  
Power Law Exponent ◽  
Axially Moving

The transverse free vibration of an axially moving beam made of functionally graded materials (FGM) is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory

2011 ◽  
Vol 225 (2) ◽  
pp. 498-506 ◽  
Author(s):  
M Mohammadimehr ◽  
A R Saidi ◽  
A Ghorbanpour Arani ◽  
A Arefmanesh ◽  
Q Han
Keyword(s):  
Elastic Medium ◽  
Axial Compression ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Small Scale ◽  
Beam Model ◽  
Critical Buckling Load ◽  
Non Local ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Using the non-local elasticity theory, Timoshenko beam model is developed to study the elastic buckling of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium under axial compression. The non-local effects in the normal and transverse shear stress components are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals' (vdW) force between the inner and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The numerical results are reported using the non-local Timoshenko beam theory and compared with those obtained using the non-local Euler—Bernoulli beam theory. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. Furthermore, in order to estimate the non-local critical buckling load of DWCNTs under axial compression, a simplified analysis is carried out and the results are compared with those obtained using molecular mechanics.

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