中文摘要：

一个近似方法为学习在步下面的双 walled 碳 nanotubes (DWNT ) 的动态弄弯在这篇论文被介绍轴的负担。分析基于连续统力学模型，它考虑在外部、内部的 nanotubes 之间的货车 der Waals 相互作用。一个弄弯的条件被导出，从哪个批评弄弯负担和联系弄弯的模式能被决定。作为例子，数字结果在固定边界条件下面为 DWNT 被得出。当把一个内胎插入到围单人赛的时，由于货车 der Waals 力量的效果， DWNT 的批评弄弯负担被提高，这被显示出。纸显示为动态弄弯的 DWNT 的批评弄弯负担为静态的弄弯比那高。半径的效果也被检验。另外，一些结果与以前的相比。

英文摘要：

A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube （DWNT） can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.