| We recently presented a micromachined doubly clamped vibrating beam sensor for measuring viscosity and density of liquids. The beam vibrations are excited by Lorentz forces arising from a sinusoidal current through an integrated conductive path. An optical readout allows determining the phase shift between the excitation current and the actual beam deflection. The interaction between the vibrating beam and the surrounding liquid alters the resonance behavior. In a modeling approach, a simple harmonic oscillator model was fit to the beam's frequency response. However, this model does not account for the frequency dependence of the liquid loading. An improved model based on the hydrodynamic function of a beam with rectangular cross-section has been fit to the measurement results. The resulting parameters yield a very high intrinsic damping parameter, indicating the presence of other damping effects not yet considered by the model. |