Energy constraints in vortex-excited vibrations

Excitation or damping of flow-induced vibrations depends upon the magnitude and the phase relationship between the fluid dynamic force and the oscillatory motion of the body. These have been measured for two aerofoil shapes in mechanically controlled heaving motion in a water channel. At the same time, measurements have been made of the strength and spacing of the associated vortex trails. To help interpret the significance of these measurements, an analysis based upon energy conservation has been performed. When taken together with the classical momentum equation, this yields a relationship giving the energy available for vibration work in terms of three dimensionless vortex trail parameters. Comparing this analysis with the experimental data leads to a qualitative discussion of the significance of the vortex formation mechanism in controlling the excitation or damping of that class of vibrations which is affected by vortex shedding.