Efficient numerical modeling of oscillatory fluid-structure interaction

We present a method to calculate the complex-valued coefficients of fluid loading of immersed mechanical resonators, used as sensors for density, viscosity, and viscoelastic properties. Based on the eigenmode decomposition of structures of arbitrary geometry, the linearized Navier-Stokes equations in the surrounding fluid are used. A complete numerical solution with finite elements is computationally very expensive for most real cases. The critical part is the fine discretization in the boundary layer. In domains away from the oscillating structure, the velocity field can be well approximated by potential flow. We introduce a novel reduced-order model for the fluid interaction which is based on the definitions of an effective added fluid volume, an effective area of shear-wave interaction, and an effective length of viscous interaction. These LAV-parameters are characteristic for a specific resonator geometry and eigenmode, and only weakly dependent on the fluid properties and frequency, so they can be used as the sensor´s calibration factors.