Flexural Instability of Viscoelastic Spinning Cylinders Partially Filled With Liquid

This paper deals with the determination of free vibration characteristics and instability conditions of flexible spinning cylinders partially filled with fluid. Using the linearized Navier–Stokes equations for the incompressible, inviscid flow, a 2D model is developed for fluid motion at each section of the cylinder. The forces exerted on the cylinder wall as a result of the fluid motion are calculated as functions of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the cylinder are derived and then combined with the equations describing the fluid forces to obtain the coupled field equations of the structural motion and the liquid sloshing dynamics. Using the obtained model, the free vibration and the stability conditions of the cylinder as well as the effect of material viscoelasticity on the stability boundaries are examined. The results of the stability analysis are presented for a number of examples, and some conclusions are outlined.