Question

A microfabricated accelerometer has an inertial mass suspended by a single silicon beam clamped at one end. The proof mass of the accelerometer, suspended at the free end, measures1 mm × 1 mm × 400 μm and the suspension beam has dimensions l = 1 mm, w = 100 μm, and t = 10 μm. Young’s modulus of silicon is E =1.9 x 1011 N/m^2. Assume there is no gravity and ignore the mass of the suspension beam. If the proof mass weighs 1.6 mg, calculate: (i) The resonant frequency of the accelerometer, (ii) The static sensitivity of the accelerometer, (iii) The deflection of the proof mass for an applied acceleration of 1 m/s^2

Answer 1

i) Using the beam formula we get the cantilever beam equivalent stiffness as

Hence

The natural frequency is given by

Therefore the resonant frequency is

ii) The static sensitivity is

iii) The deflection for applied accleration of 1 m/s² is given by