磁场环境下黏弹性基体中非局部纳米梁动力学特性分析

Dynamic analysis of nonlocal nanobeams resting on viscoelastic foundation subjected to a magnetic field

根据非局部Euler梁理论建立了外部磁场影响下的黏弹性基体上纳米梁的动力学问题分析模型。通过引入Kelvin黏弹性地基模型和洛伦兹力,得到了纳米梁的振动控制方程。基于Kelvin-Voigt黏弹性模型,给出了黏弹性基体上纳米梁在磁场影响下的固有频率解析解,并就多种典型情况进行了分析。在一般情况下,利用传递函数方法对振动控制方程进行求解,得到了纳米梁固有频率及相应振型的封闭解。以某单壁碳纳米管为例,计算得到了多种边界条件下纳米梁的前三阶固有频率,并详细分析了非局部参数、磁场强度、长细比、阻尼系数及边界条件等因素对纳米梁振动特性的影响情况。结果表明,文中所建的动力学分析模型对研究磁场作用下纳米梁在黏弹性基体上的动力学特性问题准确有效。

Based on nonlocal Euler-Bernoulli beam theory,the dynamic characteristics analysis model for nanobeams resting on viscoelastic foundation and subjected to a magnetic field was built.The Kelvin viscoelastic foundation model and the Lorentz magnetic force were introduced to derive the governing equations of the system.The new general analytical expressions for the complex natural frequencies of the nanobeams were obtained on the basis of the Kelvin-Voigt model and some typical special cases were also discussed.Then the governing equations of motion were solved by using the transfer function method to obtain the natural frequencies and corresponding mode shapes in closed form for the nanobeams with arbitrary boundary condition.Considering a single-walled carbon nanotube as a numerical example,the first three natural frequencies under various boundary conditions were obtained,and a detailed parametric study was conducted to examine the effect of nonlocal parameter,the strength of the magnetic field,the aspect ratio,the damping parameter and the boundary conditions on the vibration characteristics of nanobeams.The results demonstrate the efficiency of the proposed model for dynamic characteristics analysis of the nanobeams resting on viscoelastic foundation under a magnetic field.