Finite Amplitude Underwater Torsional Vibrations of Cantilevers

Abstract

In this paper, we analyze nonlinear torsional vibrations of thin rectangular cross section cantilever beams undergoing moderately large base excitation within a quiescent viscous fluid. The structure is modeled as a linear Euler-Bernoulli beam while the distributed hydrodynamic loading acting on the vibrating structure is described via a nonlinear complex valued hydrodynamic function which incorporates added mass and fluid damping caused by moderately large rotations. Results of a two dimensional computational fluid dynamics parametric analysis of a pitching rigid lamina, representative of a generic beam cross section, are employed to study the dependence of the hydrodynamic function on the governing flow parameters. We find that, as the frequency and amplitude of the oscillation increase, vorticity shedding and convection increase, thus resulting into nonlinear hydrodynamic damping. We derive a tractable form for the hydrodynamic function suitable for studying the nonlinear fluid-structure interactions in large amplitude torsional underwater vibrations. We establish a reduced order nonlinear modal model based on these findings and we validate theoretical predictions against experimental results on underwater torsional vibrations of flexible cantilevers.Copyright © 2012 by ASME