黏弹性基底上阻尼碳纳米管的动力学特性  

Dynamic characteristics of damped carbon nanotubes on viscoelastic foundations

作　　者：张大鹏[1] 雷勇军[1] 

机构地区：[1]国防科技大学航天科学与工程学院,湖南长沙410073

出　　处：《国防科技大学学报》2015年第6期141-149,共9页Journal of National University of Defense Technology

基　　金：国家自然科学基金资助项目(11272348;11302254)

摘　　要：采用欧拉梁模型建立了有阻尼碳纳米管在黏弹性基底上的动力学问题分析模型。通过引入非局部理论、广义Maxwell黏弹性模型、速度相依的外阻尼模型及黏弹性基底模型推导出碳纳米管动力学分析的欧拉梁振动控制方程。在Kelvin-Voigt黏弹性模型基础上,分别给出无基底和全基底支撑时碳纳米管固有频率的一般解析表达式,并分析讨论全基底时的多种典型情况。然后利用传递函数方法求解出一般边界条件下振动控制方程的封闭解。以某单壁碳纳米管为例,得到不同边界条件下该单壁碳纳米管的前四阶固有频率,并分析了碳纳米管非局部参数、黏弹性参数、基底刚度及长度等影响因素对固有频率和阻尼因子的影响情况。结果表明,文中所建的动力学分析模型及计算方法对解决碳纳米管在黏弹性基底上的动力学问题准确有效。The dynamic characteristic analysis model of damped carbon nanotubes on viscoelastic foundations was built by using Euler-Bemoulli beams. The nonlocal viscoelastic theories, general Maxwell viscoelastic model, velocity-dependent external damping model and viscoelastic foundation model were employed to deduce the governing equation of Euler-Bernouni beams for dynamic characteristics analysis of carbon nanotubes. On the basis of Kelvin-Voigt model, new general analytical expressions for the natural frequencies of damped carbon nanotubes with no foundation and full foundation were obtained respectively and some typical special cases at full foundation were discussed. Then a transfer function method was developed to obtain a closed-form and uniform solution for the vibration governing equation under arbitrary boundary conditions. Considering a single-walled carbon nanotube as a numerical example, the first four natural frequencies with different boundary conditions were obtained, and the effects of the nonlocal and viscoelastic constants, the foundation stiffness coefficient and length on the natural frequencies and damping factors were analyzed. Results demonstrate the efficiency of the proposed model and the analysis methods in solving dynamic problems of damped carbon nanotubes on viscoelastic foundations.

关 键 词：动力学特性 黏弹性基底 欧拉梁 非局部弹性理论 传递函数方法 

分 类 号：O343[理学—固体力学]