scholarly journals Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Maria Anna De Rosa ◽  
Maria Lippiello
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Van Der Waals ◽  
Beam Theory ◽  
Van Der Waals Forces ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Euler Bernoulli Beam

The free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called “cell discretization method” (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement.

On Primary Resonance of Electrostatically Actuated Double Walled Carbon Nanotube Cantilever Biosensors

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Van Der Waals Forces ◽  
Mass Sensing ◽  
Electrostatically Actuated ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper investigates electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilever biosensors using the Method of Multiple Scales (MMS) and the Harmonic Balance Method (HBM). Forces acting on the outer tube of the DWCNT are electrostatic, damping, and van der Waals, while only van der Waals acts on the inner tube. The electrostatic actuation is provided by a soft AC voltage. Van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes; herein, for modal coordinate transformation, only the linear term of the van der Waals force will be considered. The nonlinearity of the motion is produced by the electrostatic and van der Waals forces. The DWCNT undergoes nonlinear parametric dynamics. MMS is employed to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of primary resonance. DWCNTs are modelled after the Euler-Bernoulli cantilever beam. The expected nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.

Investigation of the Fundamental Frequency of Double Walled Carbon Nanotubes Using Molecular Mechanics Approach by an Averaging Van Der Waals Forces Modeling

2011 ◽  
Author(s):  
Ehsan Asadi ◽  
Ali Karimzade ◽  
Mehrdad Farid
Keyword(s):  
Carbon Nanotubes ◽  
Aspect Ratio ◽  
Molecular Mechanics ◽  
Fundamental Frequency ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Covalent Bonds ◽  
Fundamental Frequencies ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Carbon nanotubes have received a lot of attention since their introduction in 1991 because of novel properties that show substantial promises for use in many applications. Their usage depends on the strength of our knowledge of their properties. In this work, molecular mechanics approach is used to study the mechanical properties of multi-wall carbon nanotubes. In particular this paper investigates fundamental frequency of double walled carbon nanotubes. Carbon nanotubes are big and long molecules that can be regarded as mechanical structures. In modeling of multi-walled carbon nanotubes, two distinct atomic bonds are required to be modeled, i.e. covalent bonds between the neighboring carbon atoms in the same layer and Van der Waals bonds between close atoms in neighboring layers. In this approach, for modeling of each wall; covalent bonds are modeled by beam joints such that atoms are considered to be concentrated masses at the ends. Interactions of neighboring walls that are mainly due to Van der Waals forces are treated to be truss rods in modeling. The most challenging aspect of modeling is to define truss rod properties as they are highly nonlinear. We utilized an averaging method for finding truss rod properties. Finite Element Method is employed to obtain Fundamental frequencies. Results are compared to available researches and a close agreement is observed. Results indicate that by increasing aspect ratio, fundamental frequency of double walled nanotubes decrease. In addition, double walled carbon nanotubes have higher fundamental frequencies at clamp-clamp in comparison to clamp-free condition; however, this difference becomes negligible as aspect ratio increases.

Large Amplitude Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory

2015 ◽  
Vol 764-765 ◽  
pp. 1199-1203 ◽  
Author(s):  
Tai Ping Chang
Keyword(s):  
Magnetic Field ◽  
Free Vibration ◽  
Nonlocal Elasticity ◽  
Beam Theory ◽  
Nonlinear Frequency ◽  
Bernoulli Beam ◽  
Nonlinear Free Vibration ◽  
Vibration Behavior ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen's nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton's principle is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán's nonlinear strain–displacement relationships. An approximate analytical solution is obtained for the nonlinear frequency of the nanobeam under magnetic field by using the Galerkin method and He's variational method. In the numerical results, the ratio of nonlinear frequency to linear frequency is presented. The effect of nonlocal parameter on the nonlinear frequency ratio is studied; furthermore, the effect of magnetic field on the nonlinear free vibration behavior of nanobeam is investigated.

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