磁场对粘弹性基体上变截面纳米梁振动特性的影响分析

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (4) : 116-122.

论文

张大鹏，雷勇军，申志彬

作者信息 +

Effect of magnetic field on dynamic responses of nonuniform nanobeams resting on a viscoelastic foundation

ZHANG Da-peng, LEI Yong-jun, SHEN Zhi-bin

Author information +

文章历史 +

摘要

针对磁场影响下的粘弹性基体上变截面纳米梁进行了动力学建模及振动特性影响分析。首先，基于非局部欧拉梁理论、Kelvin粘弹性地基模型及麦克斯韦关系式，建立了系统的振动控制方程。然后，通过联合传递函数法和摄动法对所建振动控制方程进行求解，得到了任意边界条件下变截面纳米梁的固有频率。在此基础上，系统地分析了非局部参数、磁场强度、松弛时间、锥度系数等对阻尼频率和阻尼比的影响情况。结果表明，文章所建的动力学模型在研究受磁场影响下的粘弹性基体上变截面纳米梁的振动特性问题准确有效。

Abstract

The dynamic model was established and vibration responses were examined for a nonuniform nanobeam, which was resting on a viscoelastic foundation and subjected to a magnetic field. Based on nonlocal Euler-Bernoulli beam theory, Kelvin viscoelastic foundation model and Maxwell relation, the governing equations of the system were derived. The natural frequencies of the nonuniform nanobeams were then obtained by solving the governing equations via transfer function method incorporating with perturbation method. Subsequently, the influences of nonlocal parameter, the strength of the magnetic field, relaxation time and taper parameter on the damped frequencies and damping ratios were examined. The results show that the proposed model is available for dynamics analysis of a nonuniform nanobeam resting on a viscoelastic foundation in a magnetic field.

导出引用

张大鹏，雷勇军，申志彬. 磁场对粘弹性基体上变截面纳米梁振动特性的影响分析[J]. 振动与冲击, 2018, 37(4): 116-122

ZHANG Da-peng, LEI Yong-jun, SHEN Zhi-bin. Effect of magnetic field on dynamic responses of nonuniform nanobeams resting on a viscoelastic foundation[J]. Journal of Vibration and Shock, 2018, 37(4): 116-122

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