Fluid impedance model for immersed resonators with rectangular cross-section
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Electromechanical resonators are used as viscosity sensors where the effect of the fluid loading on the resonance parameters is
evaluated. Cantilever, tuning fork, or suspended plate geometries can be designed for a desired range and sensitivity to viscosity
and density. A complete numerical analysis of a resonator design is often not feasible due to the large computational effort. We
introduce a reduced-order fluid impedance model valid for a large class of geometries. The fluid structure interaction is characterized
by three parameters, an effective volume, an effective interaction surface, and an effective length, denoted as the LAV parameters.
For idealized geometries these parameters can be derived analytically. For general cases they are calculated from linear finite
element analysis. We derive scaling laws based on finite elements analysis for rectangular cross sections which are relevant for
cantilevers, tuning fork, and suspended plate resonators. The application of this model is on the one hand the tailoring to specified
viscosity range and sensitivity, and the evaluation of measurement data on the other hand.