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Investigation On The Dynamic Behavior Of Mulit-walled Carbon Nanotubes

Posted on:2006-02-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:F H ShaFull Text:PDF
GTID:1101360155974351Subject:Solid mechanics
Abstract/Summary:PDF Full Text Request
The discovery of the first carbon nanotube (Iijima, 1991) has attracted wide attention and stimulated extensive studies. The studies showed that the carbon nanotubes exhibit superior mechanical, electronic and chemical properties. For the use purposes of carbon nanotubes, the mechanical models are needed to understand nano-structure material properties and their effect on the mechanical behavior. On the mechanical behavior, the carbon nanotubes possess exceptionally high strength, stiffness and elastic modulus .The estimated modulus of the carbon nanotube may reach as high as 1Tpa. It is the highist of all known materials, no matter strength or stiffness higher than any known fiber. The carbon nanotubes are used as composite material reinforcement to present excellent strength, resiliency and resistance to fatigue. It would be expected that composites materials reinforced by carbonnanotubes will bring a revolution of composite materials.At present the experimental and numerical simulated methods are mainly employed in the mechanical properties investigation of the carbon nanotubes. All numerical modeling methods consist of both continuum models and atomistic models. When the molecular-dynamics (MD) methods and mixed methods based on the molecular-dynamics are used in the investigation of mechanical behavior of the carbon nanotubes, numerical modeling is confined by processing capability of computers because the total degree of freedom is huge. It is difficult to use directly MD methods in simulating nano-devices and the properties of full system. Yakobson etc compared the results of atomistic modeling for axially compressed buckling of a single-walled nanotube with the results of simple continuum models. It is found that all buckling modal shapes displayed by the molecular -dynamics models can also be predicted by the continuum model. Their results together with many others indicate that continuum models will still play an essential role in the study of carbon nanotubes.The dynamic response of the carbon nanotube represents a basic mechanical property of carbon nanotube. Although there are many results of studies on mechanical properties of the carbon nanotubes, the results of the studies of the dynamic properties are few. The van der Waals forces between adjacent nanotube have a crucial effect on mechanical behaviors of carbonnanotubes. The combined effects of the surrounding elastic medium make the question more complex.The continuum model for studying dynamic buckling behavior subjected to an axial periodic disturbance and impact torque is developed in this paper. The investigation of wave propagation along an individual multi-walled carbon nanotube is presented by a multiple-elastic-shell model. The researches are outlined as following:1. The dynamic buckling of a multi-walled carbon nanotube subjected to an axial periodic disturbanceThe dynamic response of a multi-walled carbon nanotube embedded in elastic medium subjected to periodic disturbing forces is investigated. Continuum model of the investigation of the dynamic buckling of a multie-walled carbon nanotube is developed. The effect of the van der Waals forces between two tubes and the surrounding elastic medium for axial dynamic buckling are considered. The buckling model subjected to periodic disturbing forces, the critical axial strain and the critical frequencies are given. It is found that the critical axial strain of the embedded multi-walled carbon nanotube is lower than that of an embedded single-walled carbon nanotube due to the intertube van der Waals forces. The van der Waals forces and the surrounding elastic medium affect region of dynamic instability. The van der Waals forces increase the critical frequencies of a double-walled carbonnanotube. The effect of the surrounding elastic medium for the critical frequencies is smaller.For the fist time, under mutual effect of the van der Waals forces between two tubes and the surrounding elastic medium, the buckling model subjected to periodic disturbing forces, the critical axial strain and the critical frequencies are given.2. Investigation of the dynamic buckling in the carbon nanotube under impact torqueContinuum model is developed about the investigation of the torional buckling of a double-walled carbon nanotube in this dessertation. The effect of the van der Waals forces between two tubes and the surrounding elastic medium for the torional buckling are studied. It is found that the critical forces of the embedded multi-walled carbon nanotube due to the intertube van der Waals forces are lower than that of an embedded single-walled carbon nanotube. The dynamic buckling in single-wall carbon nanotube subjected to impact torque is investigated. A single-wall carbon nanotube is modeled an elastic cylindrical shell with semi-infinite length. The dynamic buckling under impact torque is reduced to a bifurcation problem caused by propagation of torsion stress wave. The bifurcation problem can be converted to solving a group of nonlinear equations. The numerical computation is carried out, and the effects of the difference parameters on the dynamic buckling are discussed.It is found that a single-wall carbon nanotube has very much powerful anti-impact torque, the critical buckling shearing stress can reach up to a few hundreds GPa.For the fist time, the dynamic buckling displacement mode in single-wall carbon nanotube subjected to impact torque and the bifurcation problem of a group of nonlinear equations is given. The numerical computation is carried out, and the effects of the difference parameters on the dynamic buckling are given. It is found that a single-wall carbon nanotube has very much powerful anti-impact torque, the critical buckling shearing stress can reach up to a few hundreds GPa. 3. Wave propagation in multi-walled carbon nanotubesA multiple-walled-elastic-shell model is presented for wave propagation along an individual multi-walled carbon nanotube. The analysis is based on a continuum mechanics model in which each tube of a multi-walled carbon nanotube is modeled as an individual elastic shell, and its governing equation is based on Donnell's equation. The interlayer friction between any two adjacent tubes is negligible, and the van der Waals interaction between any two adjacent tubes is taken into account for coupling. The analysis shows that there exist N critical frequencies (within tetrahertz range) for an N-walled carbon nanotube. When the disturbing frequency is lower than all critical frequencies of a multi-walled carbon nanotube, vibration mode of each pointon the middle surfaces of shells has no sign change, vibration mode is coaxial and a single-elastic-shell model seems to be suitable to describe multi-walled carbon nanotubes. However, numerical results reveal that when the frequency is higher than at least one of the critical frequencies of a multi-walled carbon nanotube, some vibration modes have a sign change and waves propagate at various speeds significantly higher or lower than the speed predicted by a single-elastic-shell model. Vibration mode is noncoaxial. This phenomenon takes source at the presence of the van der Waals interaction forces. In particular, terahertz wave in multi-walled carbon nanotubes propagate at various speeds, depending not only on the frequency but also on the noncoaxial vibration modes.For the fist time, a multiple-walled-elastic-shell model is given for wave propagation along an individual multi-walled carbon nanotube. Numerical results reveal that there exist N critical frequencies (within tetrahertz range) for an N-walled carbon nanotube. When the disturbing frequency is lower than all critical frequencies of a multi-walled carbon nanotube, vibration mode is coaxial. When the frequency is higher than at least one of the critical frequencies of a multi-walled carbon nanotube, vibration mode is noncoaxial.
Keywords/Search Tags:carbon nanotube, dynamic buckling, van der Waals forces, elastic medium, multiple-elastic-shell model, wave propagation, vibration mode
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