基于两相积分模型非线性弹性基底上轴向运动纳米梁的自由振动  

Free Vibration of Axially Moving Nano-Beam with Nonlinear Foundation Based on Two-Phase Non-Local Integral Modelling

作　　者：王勇 汪洋 陈奕羽 王元斌 WANG Yong;WANG Yang;CHEN Yiyu;WANG Yuanbin(School of Mathematics,Physics and Information Science,Shaoxing University,Shaoxing,Zhejiang 312000)

机构地区：[1]绍兴文理学院数理信息学院,浙江绍兴312000

出　　处：《绍兴文理学院学报》2023年第8期44-53,120,共11页Journal of Shaoxing University

摘　　要：利用两相非局部积分模型,研究弹性基底上轴向运动纳米梁的线性振动.利用哈密顿原理,得到非局部纳米梁在固定和简支边界条件下梁的积分-微分方程模型.分析各参数对纳米梁的临界速度和固有频率的影响.结果表明梁的临界速度和固有频率在不同边界条件下,会随着非局部参数和几何参数的增大而增加;第一临界速度随着基底弹性系数的增加而减少.The present paper investigates the free vibration of axially moving nano-beam with the nonlinear foundation based on the two-phase non-local integral modelling.The integral-differential governing equation of vibration for the non-local nano-beam under simply-supported and fixed boundary condition were obtained through the Hamilton Principle.Effects of system parameters on the critical velocity and natural frequency of beam were analyzed by the numerical method.Results show that the critical velocity and natural frequency increase with the the non-local parameter and the geometrical parameter of the beam.However,the first critical velocity will decrease with the increase of the stiff coefficient of the nonlinear foundation.

关 键 词：非局部积分模型 临界速度 固有频率 弹性基底 轴向运动 

分 类 号：O322[理学—一般力学与力学基础]