Hydrodynamic Damping of Beam Oscillations near a Surface

The hydrodynamic action on long thin beams executing bending resonance vibrations in a fluid near a plane rigid surface (surface) is investigated. The model of quasi-two-dimensional interaction between the fluid and the beam is used, according to which the hydrodynamic action on any beam cross-section can regarded as a result of plane flow around it. The fluid flow in the planes orthogonal to the beam plane is modeled using the time-dependent system of Navier—Stokes equations, whose solution is determined numerically on the basis of the finite volume method. The solutions are determined in a wide range of the governing parameters of the oscillation process, namely, the dimensionless frequency, the vibration amplitude, and the distance to the surface. The dependences for the hydrodynamic forces thus obtained are used to assess the surface effect on the vibrations of cantilevers with actual physical parameters.