Stability and dynamics of rotating coaxial cylindrical shells conveying incompressible and inviscid fluid are investigated. The interior shell is assumed to be flexible while the exterior cylinder is rigid. Using Sander’s–Koiter theory assumptions and following Hamilton’s principle, governing equations of motion are determined in their integral form. Employing the extended Galerkin method of solution, the integral equations of motion are projected to their equivalent system of algebraic equations. Fluid equations are fundamentally based on the linearized inviscid Navier–Stokes equations. Impermeability condition on the fluid and structure interface as well as the zero radial velocity component on the exterior shell give the coupled equations of motion governing the dynamics of fluid-loaded coaxial cylindrical shells. Using the coupled fluid–structural model, stability boundaries are determined for the rotating interior shell. Various parameter studies are conducted and effects of mass ratio, gap distance between the interior and exterior shells, boundary conditions of the interior shell, length to radius ratio on the stability margins are thoroughly investigated and reported.

中文翻译：

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旋转圆柱壳在环形流体介质中的动力学和稳定性分析

研究了输送不可压缩和非粘性流体的旋转同轴圆柱壳的稳定性和动力学。假设内壳是柔性的，而外圆柱体是刚性的。使用 Sander 的 Koiter 理论假设并遵循 Hamilton 原理，运动控制方程以其积分形式确定。采用扩展的 Galerkin 求解方法，将积分运动方程投影到其等效的代数方程组。流体方程基本上基于线性化的无粘性 Navier-Stokes 方程。流体和结构界面的不渗透性条件以及外壳上的零径向速度分量给出了控制流体加载同轴圆柱壳动力学的耦合运动方程。使用耦合的流体结构模型，确定旋转内壳的稳定性边界。进行了各种参数研究，并对质量比、内外壳之间的间隙距离、内壳的边界条件、长径比对稳定裕度的影响进行了深入研究和报告。