Question: The micro bridge of Figure is used to evaluate the dynamic viscosity of a fluid by transverse capacitive sensing of the midpoint displacement relative to the input displacement u = 5 sin(200t) nm of a massless cage. Use a lumped parameter model to determine the fluid dynamic viscosity knowing that the bridge has a length of 230 nm, width of 60 nm, thickness of 1.2 nm, Young's modulus of 1.6 # 1011 N/m2 , and mass density of 6100 kg/m3 . The maximum voltage sensed by the capacitor is DV = 20 nV and the mass of capacitor plate attached to the micro bridge is mp= 2 # 10-12 kg. For the capacitive sensor, the initial gap is g0 = 12 nm and the bias voltage is vb = 10 nV.
