基于修正偶应力理论和微分变换法的输流微管自由振动  

Free vibration of fluid-conveying micro-tubules using the modified couple stress theory and differential transformation method

作　　者：朱成秀 随岁寒 李成 ZHU Chengxiu;SUI Suihan;LI Cheng(School of Rail Transportation,Soochow University,215131 Suzhou,China;School of Automotive Engineering,Changzhou Insititute of Technology,213032 Changzhou,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,541004 Guilin,China)

机构地区：[1]苏州大学轨道交通学院,苏州215131 [2]常州工学院汽车工程学院,常州213032 [3]桂林电子科技大学广西密码学与信息安全重点实验室,桂林541004

出　　处：《应用力学学报》2023年第2期443-449,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.11972240);广西密码学与信息安全重点实验室研究课题(No.GCIS201905)。

摘　　要：考虑黏性流体在微管道内作层流运动,给出了黏性流体在微圆管中的速度分布方程。利用修正偶应力理论和Euler梁模型建立细长微管模型,根据虚功原理推导输流微管流-固耦合振动方程,应用微分变换法计算微管道系统的固有频率。通过与有限差分法求解结果对比,证明微分变换法具有较高的精度。随后,研究了流体黏性、微管材料内禀特征尺寸和预应力对固有频率的影响。最后,分析了流体临界流速与预应力的关系。数值结果表明:在流体平均速度相同的条件下,考虑流体黏性时微管各阶固有频率偏低,并且平均速度越大,这一趋势越明显。Considering a laminar flow of viscous fluid in micro-tubules,the velocity distribution equation of viscous fluid in a circular micro-tubule is provided.The modified couple stress theory and Euler beam model are used to develop the slender micro-tubule model,and the liquid-solid coupled vibration equation of the flow-conveying micro-tubules is derived based on the principle of virtual work.The natural frequencies of the flow-conveying micro-tubules are calculated using the differential transformation method.It is indicated that the differential transformation method is of high accuracy compared with the results obtained by the finite difference method.Subsequently,the effects of liquid viscosity,material length scale parameter and pre-stress on natural frequencies are examined.Finally,the relationship between the critical speed of fluids and the pre-stress is analyzed.From the numerical results,it can be concluded that under the condition of the same average velocity of fluids,the natural frequencies of micro-tubules become lower when considering the fluid viscosity,and the higher the average velocity is,the more obvious the downward trend of natural frequencies is.

关 键 词：黏性流体 输流微管 微分变换法 固有频率 临界流速 

分 类 号：O326[理学—一般力学与力学基础] O351[理学—力学]