碳纳米管及其复合材料的力学特性
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摘要
复合材料增强结构具有高强度、高刚度和各种优越的物理特性，越来越多地应用于航空、机械、医疗、化工等许多领域。碳纳米管具有异常优异的力学、电磁学和化学性能，在比强度和比刚度方面都远优于目前使用的其他增强纤维材料，将其作为复合材料增强体，预计可表现出良好的强度、刚度及其它物理特性，碳纳米管增强复合材料能够使得新型复合材料的物理力学性能产生一次飞跃。因此研究碳纳米管及其增强复合材料结构的物理和力学特性对于新型复合材料在工程中的应用有着重要的理论意义和实际应用价值。
本论文研究的主要内容和成果为：
（1）基于分子结构力学理论和Lennard-Jones势函数建立模拟碳纳米管力学及物理特性的空间框架模型，求解了碳纳米管的材料性质、环境温度、应变率和结构形式对其力学特性的影响，给出了相应的解析表达式，讨论了碳纳米管的管径和温度环境等对其力学性质的影响。基于分子结构力学模型的有限元模拟结果表明，双壁碳纳米管的杨氏模量随应变率的增大而升高，并随环境温度的增加急剧减小，应变率和温度环境对杨氏模量的影响依赖于多壁碳纳米管的管壁数目；不同手性单壁碳纳米管的泊松比随着环境温度的增加而增加。研究结果给出了环境条件对碳纳米管物理特性的一般影响规律，为碳纳米管的工程应用提供了理论依据。
（2）基于连续介质力学方法的Euler-Bernoulli梁和相应的层合梁模型模拟碳纳米管及其增强复合材料的振动和波传播的特性，推导了考虑任意两层间严格van derWaals力作用的碳纳米管中波传播的方程，研究了严格van der Waals力对碳纳米管中波传播特性的影响。多层梁与单一梁模型的对比表明考虑严格van der Waals力得到的碳纳米管及其复合材料的共振频率，尤其是管层间频率（inter-tube frequency），小于未考虑严格van der Waals力时的共振频率，两种梁模型在初始轴向载荷作用下的共振频率比较接近，其低阶振动模态数随着长径比增加而减少，这给碳纳米管及其复合材料在纳米驱动装置和超高频振荡器等方面的应用提供了理论参考依据。
（3）考虑纳米尺度结构的表面效应，基于严格van der Waals力的多层梁和等效的单层梁模型，推导了表面弹性模量和表面张力共同作用下碳纳米管及其复合材料中波的传播方程并给出了相应的解析解，揭示了表面效应对碳纳米管的固有频率的影响机理。研究表明碳纳米管的表面效应使碳纳米管及其复合材料振动变得更加复杂。在一定条件下，表面效应使低阶固有频率降低，低阶振动模态相应减少，多层梁和单一梁模型的数值差异性进一步扩大，因此表面效应对碳纳米管及其复合材料动态性能的影响比较明显。研究表面效应对碳纳米管的动态力学特性的影响对其作为碳纳米管高敏传感器和纳米微谐振器等的优化设计和实际应用有着重要的工程应用价值。
本文在上述研究方向上给出了一些发表的研究成果，揭示了多场作用下的碳纳米管及其复合材料结构的力学特性，对碳纳米管及其复合材料结构的静动态力学性能研究和该类结构性能的优化设计提供了有意义的理论参考和实际工程应用价值。
Composites reinforced structures are of superior performance of high strength, highstiffness, and many excellent physical characteristics, and more and more applied in manyfields of aviation, mechanics, medicine, chemistry and others. Carbon nanotubes havemany extremely excellent mechanical, electromagnetic and chemical properties, and are farsuperior to the currently used reinforced fiber materials on strength or toughness. It isexpected that the carbon nanotubes reinforced composites can bring a leap-forwarddevelopment of strength, stiffness and other physical properties of composite structures.The study of physical and mechanical characteristics of carbon nanotubes and theircomposite reinforcement have important and unique theoretical significance andengineering applications for new composite materials design.
The main works and results of this thesis include:
(1) Based on the molecular structural mechanics theory and the Lennard-Jones theory,a space frame model is established to simulate mechanical and physical properties of thecarbon nanotubes and study the effects of the material properties of carbon nanotubes,environment temperature, strain rates and structure forms and etc on its mechanicalproperties, and the corresponding analytical expressions are obtained. The finite elementsimulation results of the molecular structure mechanical model show that the Young'smodulus of double-walled carbon nanotubes increases with strain rates, and decreasesrapidly with increasing environment temperature, the effects of strain rates and temperatureenvironment on Young's modulus depends on the layer numbers of multi-walled carbon nanotubes; the Poisson's ratio of single-walled carbon nanotube of different chiral patternincreases as the environment temperature increases. The results show the general principlesof environmental conditions on the physical properties of carbon nanotubes and providetheoretical basis for the applications.
(2) An Euler-Bernoulli beam and the corresponding elastic laminated beams model isused to investigate wave propagation in carbon nanotubes and their reinforced compositestructures based on continuum mechanics. Wave propagation equations in carbonnanotubes and their reinforced composite structures are derived considering van der Waalsinteraction between any two tubes of carbon nanotubes and used in calculation andsimulation to investigate the effect of van der Waals interaction on characteristics of wavepropagation in carbon nanotubes and their reinforced composite structures. Thecomparison between laminated beam model and single beam model shows that resonancefrequencies obtained considering van der Waals interaction between any two tubes ofcarbon nanotubes are lower than those which consider van der Waals interaction onlybetween two adjacent tubes, especially the inter-tube frequencies. Furthermore, theresonant frequencies obtained by these two beam models under different initial stresses arecloser than the latter, and the number of low-order vibration mode decreases when theaspect ratio increases. The studies have theoretical significances on the applications ofcarbon nanotubes and their composite such as nano-drive devices and ultra-high-frequencyoscillator.
(3) Considering the surface effects on nano-scale structure, wave propagationequations in carbon nanotubes and their reinforced composite structures under the effectsof surface elasticity modulus and surface tension are derived and the correspondinganalytical solutions are given based on laminated beam model and the equivalent singlebeam model under van der Waals interaction between any two tubes. The results reveal thecommon influence mechanism of surface effects on the natural frequency of the carbonnanotubes and their reinforced composite structures. The studies show that the vibration of carbon nanotubes and their composites becomes more complex considering surface effects.Under certain conditions surface effects may decrease natural frequency and the number oflow-order vibration mode, and the difference in resonance frequency between laminatedbeam model and single beam model is wider while considering the surface effects. Theinvestigations of surface effects on the dynamic properties of carbon nanotubes and theircomposites have theoretical values on optimal designs and engineering applications ofcarbon nanotubes and their composite as nano-micro-resonators and high sensitivitysensors.
Many researches have been published in the above fields and reveal mechanicalproperties of carbon nanotubes and their composite structures subjected to coupled fields.It is very meaningful for researches on static and dynamic mechanical properties of carbonnanotubes and their composite structures and the optimal design of the structuralperformance on theoretical reference and engineering value.
本论文研究的主要内容和成果为：
（1）基于分子结构力学理论和Lennard-Jones势函数建立模拟碳纳米管力学及物理特性的空间框架模型，求解了碳纳米管的材料性质、环境温度、应变率和结构形式对其力学特性的影响，给出了相应的解析表达式，讨论了碳纳米管的管径和温度环境等对其力学性质的影响。基于分子结构力学模型的有限元模拟结果表明，双壁碳纳米管的杨氏模量随应变率的增大而升高，并随环境温度的增加急剧减小，应变率和温度环境对杨氏模量的影响依赖于多壁碳纳米管的管壁数目；不同手性单壁碳纳米管的泊松比随着环境温度的增加而增加。研究结果给出了环境条件对碳纳米管物理特性的一般影响规律，为碳纳米管的工程应用提供了理论依据。
（2）基于连续介质力学方法的Euler-Bernoulli梁和相应的层合梁模型模拟碳纳米管及其增强复合材料的振动和波传播的特性，推导了考虑任意两层间严格van derWaals力作用的碳纳米管中波传播的方程，研究了严格van der Waals力对碳纳米管中波传播特性的影响。多层梁与单一梁模型的对比表明考虑严格van der Waals力得到的碳纳米管及其复合材料的共振频率，尤其是管层间频率（inter-tube frequency），小于未考虑严格van der Waals力时的共振频率，两种梁模型在初始轴向载荷作用下的共振频率比较接近，其低阶振动模态数随着长径比增加而减少，这给碳纳米管及其复合材料在纳米驱动装置和超高频振荡器等方面的应用提供了理论参考依据。
（3）考虑纳米尺度结构的表面效应，基于严格van der Waals力的多层梁和等效的单层梁模型，推导了表面弹性模量和表面张力共同作用下碳纳米管及其复合材料中波的传播方程并给出了相应的解析解，揭示了表面效应对碳纳米管的固有频率的影响机理。研究表明碳纳米管的表面效应使碳纳米管及其复合材料振动变得更加复杂。在一定条件下，表面效应使低阶固有频率降低，低阶振动模态相应减少，多层梁和单一梁模型的数值差异性进一步扩大，因此表面效应对碳纳米管及其复合材料动态性能的影响比较明显。研究表面效应对碳纳米管的动态力学特性的影响对其作为碳纳米管高敏传感器和纳米微谐振器等的优化设计和实际应用有着重要的工程应用价值。
本文在上述研究方向上给出了一些发表的研究成果，揭示了多场作用下的碳纳米管及其复合材料结构的力学特性，对碳纳米管及其复合材料结构的静动态力学性能研究和该类结构性能的优化设计提供了有意义的理论参考和实际工程应用价值。
Composites reinforced structures are of superior performance of high strength, highstiffness, and many excellent physical characteristics, and more and more applied in manyfields of aviation, mechanics, medicine, chemistry and others. Carbon nanotubes havemany extremely excellent mechanical, electromagnetic and chemical properties, and are farsuperior to the currently used reinforced fiber materials on strength or toughness. It isexpected that the carbon nanotubes reinforced composites can bring a leap-forwarddevelopment of strength, stiffness and other physical properties of composite structures.The study of physical and mechanical characteristics of carbon nanotubes and theircomposite reinforcement have important and unique theoretical significance andengineering applications for new composite materials design.
The main works and results of this thesis include:
(1) Based on the molecular structural mechanics theory and the Lennard-Jones theory,a space frame model is established to simulate mechanical and physical properties of thecarbon nanotubes and study the effects of the material properties of carbon nanotubes,environment temperature, strain rates and structure forms and etc on its mechanicalproperties, and the corresponding analytical expressions are obtained. The finite elementsimulation results of the molecular structure mechanical model show that the Young'smodulus of double-walled carbon nanotubes increases with strain rates, and decreasesrapidly with increasing environment temperature, the effects of strain rates and temperatureenvironment on Young's modulus depends on the layer numbers of multi-walled carbon nanotubes; the Poisson's ratio of single-walled carbon nanotube of different chiral patternincreases as the environment temperature increases. The results show the general principlesof environmental conditions on the physical properties of carbon nanotubes and providetheoretical basis for the applications.
(2) An Euler-Bernoulli beam and the corresponding elastic laminated beams model isused to investigate wave propagation in carbon nanotubes and their reinforced compositestructures based on continuum mechanics. Wave propagation equations in carbonnanotubes and their reinforced composite structures are derived considering van der Waalsinteraction between any two tubes of carbon nanotubes and used in calculation andsimulation to investigate the effect of van der Waals interaction on characteristics of wavepropagation in carbon nanotubes and their reinforced composite structures. Thecomparison between laminated beam model and single beam model shows that resonancefrequencies obtained considering van der Waals interaction between any two tubes ofcarbon nanotubes are lower than those which consider van der Waals interaction onlybetween two adjacent tubes, especially the inter-tube frequencies. Furthermore, theresonant frequencies obtained by these two beam models under different initial stresses arecloser than the latter, and the number of low-order vibration mode decreases when theaspect ratio increases. The studies have theoretical significances on the applications ofcarbon nanotubes and their composite such as nano-drive devices and ultra-high-frequencyoscillator.
(3) Considering the surface effects on nano-scale structure, wave propagationequations in carbon nanotubes and their reinforced composite structures under the effectsof surface elasticity modulus and surface tension are derived and the correspondinganalytical solutions are given based on laminated beam model and the equivalent singlebeam model under van der Waals interaction between any two tubes. The results reveal thecommon influence mechanism of surface effects on the natural frequency of the carbonnanotubes and their reinforced composite structures. The studies show that the vibration of carbon nanotubes and their composites becomes more complex considering surface effects.Under certain conditions surface effects may decrease natural frequency and the number oflow-order vibration mode, and the difference in resonance frequency between laminatedbeam model and single beam model is wider while considering the surface effects. Theinvestigations of surface effects on the dynamic properties of carbon nanotubes and theircomposites have theoretical values on optimal designs and engineering applications ofcarbon nanotubes and their composite as nano-micro-resonators and high sensitivitysensors.
Many researches have been published in the above fields and reveal mechanicalproperties of carbon nanotubes and their composite structures subjected to coupled fields.It is very meaningful for researches on static and dynamic mechanical properties of carbonnanotubes and their composite structures and the optimal design of the structuralperformance on theoretical reference and engineering value.
引文
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