Abstract

Steady flow of a viscous fluid around a transversely oscillating, simply-supported beam is driven by forces represented in the nonlinear terms of the Navier-Stokes’ equation. This flow occurs inside and outside the viscous boundary layer. The flow-velocity amplitude is proportional to the square of the amplitude of the beam transverse velocity and thus it is essentially only observable during high velocity beam vibration. This flow, known as ‘edge streaming’, does not occur in an ideal fluid. In the flow the fluid is ‘drawn in’ at the edges of the beam near the vibrational antinodal points and ‘expelled’ at the nodal points. When a rigid plate is placed parallel to the long axis of the vibrating beam and normal to the vibration velocity, vortices of different orientation are generated depending on the separation of the plate and beam surfaces. When the separation is an order of magnitude greater than the boundary layer thickness, the vortices have the rolling characteristic discussed by Rayleigh [1]. But for small separation of the order of the boundary layer thickness, the vortical axes are perpendicular to that of the former, parallel to the vibration velocity. They have been experimentally observed [6]. Owing to the streaming motion, damping, as measured by the ratio of the dissipation of energy and the total vibration energy over a time period, has a nonlinear hard representation with respect to the vibration amplitude.

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