黏弹性基底上阻尼碳纳米管的动力学特性

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。

Dynamic characteristics of damped carbon nanotubes on viscoelastic foundations

The dynamic characteristics of damped carbon nanotubes on viscoelastic foundations are studied using Euler-Bernoulli beams in this paper. The nonlocal viscoelastic theories and general Maxwell model, velocity-dependent external damping and viscoelastic foundation model are employed to establish the governing equation of Euler-Bernoulli beams for dynamic characteristics analysis of carbon nanotubes. Based on Kelvin-Voigt model, new general analytical expressions for the natural frequencies of damped carbon nanotubes are obtained respectively with no foundation and full foundation, and some typical special cases are discussed for full foundation. Then a tranfer function method (TFM) is developed to obtain closed-form and uniform solution for the vibration analysis of the damped carbon nanotubes resting on the viscoelastic foundations with arbitrary boundary conditions. Considering a single-walled carbon nanotube (SWCNT) as a numerical example, the first four natual frequencies with different boundary conditions are obtained, and the effects of the nonlocal and viscoelastic constants, the foundation stiffness coefficient and length on the natural frequencies and damping factors are discussed. The results demostrate the efficiency of the proposed modeling and analysis methods for dynamic characteristics of damped carbon nanotubes on viscoelastic foundations.