基于修正偶应力理论和微分变换法的输流微管自由振动

Subjects: Mechanics >> Basic Mechanics submitted time 2023-04-24 Cooperative journals: 《应用力学学报》

朱成秀 随岁寒 李成

Abstract：
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.

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