Theoretical model on the interaction of a vibrating beam and the surrounding viscous fluid with applications to density and viscosity sensors

A new theoretical model on the frequency response of a vibrating beam immersed in a viscous fluid is developed. An integral equation is derived from the Navier-Stokes equation for an incompressible fluid, where the advection term has been neglected This equation is valid for any planar shape and characterizes the pressure distribution on the surface. The equation of a vibrating cantilever beam under the effect of a given driving force and the newly obtained fluid reaction is then solved. This method provides a means of calculating the frequency response for the Schlumberger DV-MEMS sensor.