粘弹性液体在非均质管内的流动
Flow of the Viscous-Elastic Liquid in the Non- Homogeneous Tube
摘要：
随着液体输送系统在生物体和技术中的广泛应用，波在流动液体的可变形壳体中的传播问题变得非常紧迫。在求解这类问题时，为了研究空腔内液体运动对壳体动力学的影响，必须考虑壳体的运动方程。如今，这类问题的总和是流体力学的一个广泛发展的领域。然而，考虑到液体的粘弹性和壳体材料的不均匀性，一些特殊性产生了相当大的数学困难，与变系数的边值问题的集成。本文研究了封闭在可变形管中液体的波动流动。所采用的数学模型是由不可压缩粘弹性液体的运动方程结合连续性方程和非均匀管长的动力学方程描述的。人们普遍认为，管是圆柱形的，半无限的，刚性固定到环境中。在无穷远处，管子是均匀的。最后将问题归结为Volterra型积分方程的求解问题，并采用序列逼近法求解。脉动压力在管的末端给出，以确定所需的流体动力学函数。
英文摘要：
A problem on propagation of waves in deformable shells with flowing liquid is very urgent in connection with wide use of liquid transportation systems in living organisms and technology. It is necessary to consider shell motion equations for influence of moving liquid in cavity on the dynamics of a shell by solving such kind problems. Nowadays a totality of such problems is a widely developed field of hydrodynamics. However, a number of peculiarities connected with taking into account viscous-elastic properties of the liquid and inhomogeneity of the shell material generates considerable mathematical difficulties connected with integration of boundary value problems with variable coefficients. In the paper we consider wave flow of the liquid enclosed in deformable tube. The used mathematical model is described by the equation of motion of incompressible viscous elastic liquid combined with equation of continuity and dynamics equation for a tube inhomogeneous in length. It is accepted that the tube is cylindric, semi-infinite and rigidly fastened to the environment. At the infinity the tube is homogeneous. As a final result, the problem is reduced to the solution of Volterra type integral equation that is solved by sequential approximations method. Pulsating pressure is given at the end of the tube to determine the desired hydrodynamic functions.}
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
