Nonlinear vibrations and stability of rotating cylindrical shells conveying annular fluid medium

Abstract

This study aims to investigate the nonlinear dynamic characteristics of annular cylinders coupled with a fluid medium to identify the effective parameters on stability margins at different rotation speeds. To achieve this, stability and nonlinear vibrations of rotating cylindrical shells containing incompressible annular fluid are considered. The fluid medium is bounded by a rigid external cylinder. Sanders–Koiter kinematic assumptions are utilized to determine the geometrically nonlinear structural equations of motion. These equations are then used to investigate finite amplitude vibrations of various fluid-loaded shells at different states. A penalty approach is introduced by using boundary springs with arbitrary stiffness to simulate any desired set of end conditions. Both driven and companion modes of vibration are included in the solution algorithm to capture the traveling wave response. Fluid equations are determined by using the linearized Navier–Stokes equations. The two sets of governing equations are coupled through the flow impermeability condition on the internal shell’s interface and the zero fluid particle velocity condition on the external boundary. Nonlinear numerical solutions to rotating shells with extremal fluid loading are conducted by the Runge–Kutta direct integration technique. The minimum number of driven/companion modes is determined and the results are verified with the available literature. Results show a significant exchange of energy between the driven and companion modes which consequently initiates a traveling wave response in rotating shell configurations. Moreover, the centrifugal loading and external excitation are shown to be effective on the oscillation amplitude as rotation speed changes leading to alteration of the response quality from periodic to chaotic.