论文摘要
碳纳米管因独特的分子结构和优异的物理、化学、力学性质而具有重大的应用价值。连续介质力学是研究碳纳米管力学性能的一个有效而经济的重要方法。本文基于连续介质力学理论,分别采用了三维实体模型、梁模型和壳模型研究了与碳纳米管的屈曲及振动问题相关的力学特性。本文的研究工作分为四部分。第一部分用有限元实体单元模拟了多壁碳纳米管（MWNTs）大角度弯曲时的局部屈曲现象及弯曲刚度的降低,得到了多壁碳纳米管的弯曲本构关系,并用梁单元进行了交变电场中碳纳米管的振动分析,从理论上解释了共振法测得多壁碳纳米管的杨氏模量随直径增大而减小的现象,并为实验测量碳纳米管进入非线性弯曲变形的临界应变及波纹模式弯曲刚度提供了理论依据。第二部分介绍了多层弹性壳体模型,考虑了MWNTs两相邻管间的范德华作用,分别研究了单个MWNTs的扭转屈曲和埋入弹性基体MWNTs的偏心压缩屈曲问题。针对单个MWNTs在两种不同载荷条件下的扭转屈曲特性的研究,给出了临界扭转载荷的显式表达式。结果表明,扭矩只作用在最外层管的MWNTs的临界扭转载荷值比同样条件下扭矩按剪切薄膜力与半径成比例分布在各层上的情况的值要高。该结论对于应用纳米管设计微驱动机电装置、扭转震荡器等纳米结构装置具有理论参考价值。本文第三部分基于Lennard-Jones模型,利用多壁碳纳米管任意两层间严格范德华作用的公式,分析了埋入弹性基体MWNTs的径向呼吸振动和热环境下MWNTs的轴向屈曲问题。结果表明,基于严格范德华作用模型的MWNTs的力学特性与简单范德华作用模型所得的值有一定差异。严格范德华作用依赖于层间距离的变化和各管半径,其MWNTs的最高径向呼吸振动频率比仅考虑两相邻管间范德华作用的频率要高;其MWNTs的轴向临界应力要比仅考虑两相邻管间范德华作用的临界应力大。第四部分以非局部连续介质力学理论为基础,利用流体-多层梁模型求解受轴向载荷,埋入基体中充液碳纳米管的耦合振动问题,考虑了碳纳米管的小尺度效应。通过具体算例与经典局部理论解的比较分别考察了各种参数条件下小尺度效应对碳纳米管振动频率的影响,指出了经典连续介质力学的适用范围。通过与无充液碳纳米管解的比较分别考察了几何形状、流体密度、基体温克勒常数、轴向载荷、层数、模态阶数等各种参数条件下流体耦合效应对充液碳纳米管动态特性的影响。本文得到的一些有意义结果揭示了碳纳米管屈曲和振动方面的新特性,有助于以碳纳米管为元件的纳米结构和装置的设计与应用。
论文目录
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