相容拉格朗日-欧拉法求解粘性流体中弹性圆柱壳的振动

采用相容拉格朗日-欧拉法，研究圆柱壳表面不间断振动时粘性流体的速度以及壳体的推进速度。根据粘性流体分子的粘附条件简化接触面条件，变形后的变量通过变形前各量的泰勒级数展开式近似表示。假设雷诺数Re < 0.1，纳维-斯托克斯方程采用斯托克斯近似，考虑弹性圆柱壳表面发生横向振动与纵向振动。结果表明，弹性圆柱壳半径增大时，流体的速度趋近于薄板振动时的结果，纯横向振动时壳的位移方向与波的方向相反，纯纵向振动时二者方向相同，两种形式的振动均有，则方向可能相同，也可能相反。
Abstract：Here, when a cylindrical shell vibrated continuously in viscous fluid, velocity of viscous fluid and the cylindrical shell’s propulsion speed were studied with the united Lagrangian-Eulerian method.The contact surface conditions were simplified according to adhesion conditions of viscous fluid molecules.Variables after deformation were approximately expressed with their Taylor series expansions before deformation.When Reynolds number Re < 0.1, Navier-Stokes equations were replaced by Stokes ones to study transverse and longitudinal vibrations of the elastic cylindrical shell.The results showed that fluid velocity distribution approaches a thin plate vibration results with increase in cylindrical shell’s radius; the shell’s displacement direction is opposite to the wave’s one during shell having transverse vibration, but their directions are the same during shell having longitudinal vibration; their directions may be the same or opposite during shell having both transverse and longitudinal vibrations.