United Lagrangian-eulerian Method For The Problem Of Cylindrical Shell Vibration In Viscous Fluid

In recent years,driven by the exploration,development and utilization of marine resources,many researchers study on the movement mechanism of underwater creatures.The research on underwater propeller,involving biological discipline,fluid mechanics discipline,mechanical discipline,material control discipline and other disciplines,has wide utilization and huge potential value.Waving motion is one kind of propulsion methods adopted by the aquatic animals.The theory of propulsion is extensively studied by the scholars at home and broad.But for the complexity of the issue and the deficiency of the research,a deeper and more extensive research on the theory of propulsive is needed.The creatures in the water are seen as one elastic cylindrical shell in this paper.The coupling interaction between the elastic shell,which is advancing in waves and the viscous fluid is studied.Applied the fundamental equations of fluid mechanics and elastics theory of thin shells,and with the kinematic equation of fluid-solid contact surfaces,the stream function and pressure function are solved.Meanwhile the effects eventually aims at a more comprehensive understanding of movement of elastic body in the viscous fluid.Firstly,the kinematic equation and dynamic equation of their contact surfaces are put forward by using united Lagrangian-Eulerian method.The contacting surface conditions are simplified based on the viscous fluid adsorption.The viscous fluid velocity expressions are presented using Taylor expansion method.Secondly,the Navier-Stokes equations for incompressible viscous fluid are almost equal to the Stokes equations under the assumption of a low Reynolds number less than 1.Finally,the form of stream function is given and the elastic cylindrical shell with vibrations which performs a traveling-wave movement is considered.Based on dynamic equation of contact surface,fluid continuity equation and special function theory,the undetermined parameters of stream function are solved.Then the velocity of viscous fluid,pressure and other issues are solved.Using concrete examples,the fluid field figures are obtained,and the impact of the factors is analyzed to the velocity and the stress of fluid,which are the wave amplitude,wave form and the radius of the shell.