多参数耦合作用输流纳米管的振动分析

基于非局部Euler-Bernoulli梁模型,考虑外加纵向磁场及Pasternak弹性基体,应用哈密顿原理建立了纵向磁场作用下嵌入弹性基体中的简支输流单层碳纳米管(SWCNT)系统振动微分方程及其边界条件。应用微分变换法(DTM)求解上述微分方程,着重研究磁场强度、Pasternak弹性基体的弹性参数与剪切参数以及纳米管小尺度系数对系统临界失稳流速的影响及各参数耦合作用时参数间的相互影响。数值计算结果表明:磁场强度与弹性基体增强系统刚度,提高系统稳定性,但二者耦合作用时对系统刚度的影响表现出“此长彼消”的特点。小尺度效应降低系统刚度,相比磁场对刚度的影响,磁场的影响更为显著。小尺度效应与弹性基体的相互影响则表现出较为复杂的特点。

Vibration analysis of fluid-conveyed single-walled carbon nanotubes embedded in elastic medium under a longitudinal magnetic field

Based on nonlocal Euler-Bernoulli beam theory, vibration characteristics are investigated for a fluid-conveyed single-walled carbon nanotube (SWCNT) which is embedded in an elastic medium and subjected to a longitudinal magnetic field. Governing equations of motion are derived for vibration analysis of fluid-conveyed SWCNTs, where the Lorentz magnetic force and the surrounding elastic medium have been taken into consideration. Subsequently, differential transformation method (DTM) is employed to compute the critical fluid velocity for fluid-conveyed SWCNTs with simple supported boundary condition. The obtained results are followed by a detailed parametric study of the effects of nonlocal parameter, elastic foundation parameter and longitudinal magnetic field on the vibration of fluid-conveyed SWCNTs. Through various numerical studies, the coupling effects of nonlocal parameter, elastic foundation parameter and the strength of magnetic field on the critical fluid velocity of the fluid-conveyed SWCNT are carefully examined.