Dynamic characteristics of a beam angular-rate sensor

This paper gives a bandwidth and sensitivity analysis for a vibrating square beam angular-rate sensor. A skew-symmetric gyroscopic inertia matrix results from rotating about an axis orthogonal to the plane of a forced-vibration elastic system giving unique characteristics permitting measurement of its rotation rate. The quality factor has a huge influence on the forced response at the resonant frequencies governing the dynamic operating range in its use as an angular-rate sensor. Fourier-type solution for the cantilever beam with electrostatic excitation reveals characteristics analogous to those occurring for more complex systems. The deflection-dependent nature of the electrostatic excitation induces the parametric excitation into the system, yielding a Hill-type equation. Although it causes the behavior to be more complex, linear sensitivity curves can be obtained, provided that the displacement of the beam is small compared with the gap in static equilibrium. Finally, it is seen that the system provides the applicability of the rotating beam for use as an angular-rate sensor within a certain small range of parametric excitation. Design rules are suggested by observing that sensor sensitivity decreases with increasing sensor bandwidth.