单壁碳纳米管在非局部粘弹性基体中的振动特性研究

VIBRATION CHARACTERISTICS OF SINGLE-WALLED CARBON NANOTUBES EMBEDDED IN NON-LOCAL VISCOELASTIC MEDIUM

基于非局部弹性理论,针对非局部粘弹性基体中单壁碳纳米管的振动特性问题进行了研究。通过引入欧拉梁模型和非局部粘弹性地基模型,建立了系统的振动控制方程,并利用传递函数法得到了任意边界条件下非局部粘弹性基体中单壁碳纳米管固有频率的封闭解。以某根置于非局部粘弹性基体中的单壁碳纳米管为例,计算了不同边界条件和非局部参数下碳纳米管的前三阶固有频率,并在此基础上研究了非局部粘弹性基体主要材料参数对碳纳米管固有频率的影响特性。结果表明,所建分析模型和求解方法在分析粘弹性基体中碳纳米管的振动特性问题中准确有效。

Based on the nonlocal elasticity theory, the vibration characteristics of single-walled carbon nanotubes embedded in nonlocal viscoelastic medium are researched. The Euler-Bernoulli beam model and nonlocal viscoelastic foundation model are introduced to establish the governing equations for the vibration of the carbon nanotubes. The transfer function method is then employed to derive the natural frequencies of the embedded carbon nanotubes with arbitrary boundary conditions. Subsequently,a SWCNT embedded in nonlocal viscoelastic medium is taken as a numerical example,and the first three natural frequencies of the SWCNT are obtained for different boundary conditions and nonlocal parameters. In addition,the influences of nonlocal viscoelastic medium on the natural frequencies are examined. The results demonstrate the efficiency of the proposed modeling method for the vibration response of the SWCNTs embedded in a medium.