OSCILLATORY BEHAVIOR OF AN ELECTROSTATICALLY ACTUATED MICROCANTILEVER GYROSCOPE

This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input angular rate of the beam along its axis. The input angular rotation can be measured by sensing the oscillation tuned to another DC voltage of the proof mass. First, a system of nonlinear equations governing the flexural–flexural motion of electrostatically actuated microbeam gyroscopes subjected to input rotations is derived by the extended Hamilton principle. The oscillatory behavior of the microgyroscopes subjected to DC voltages in both directions is then analytically investigated. Finally, the effects of the geometric parameters, base rotation and fringing field on the natural frequencies of the system are assessed.

Numerical and Experimental Analysis of Monostable Mini- and Micro-Oscillators

An asymmetric micro-oscillator design based on a monostable fluidic amplifier is proposed. Experimental data with various feedback loop configurations point out that the main effect responsible for the oscillation is a capacitive and not a propagative effect. Actually, sound propagation in the feedback loop only generates a secondary oscillation which is not strong enough to provoke the jet switching. Data from a hybrid simulation using a commercial CFD code and a simple analytical model are in good agreement with the experimental data. A more compact plane design with reduced feedback loop volumes is also studied through a fully CFD simulation that confirms the previous conclusions.

Inertial oscillations in a rotating fluid cylinder

A study is described of the forced inertial oscillations appearing in an axially rotating completely filled circular cylinder with plane ends. Excitation is provided by causing the top end to rotate about an axis inclined slightly to the rotation axis. Experiments demonstrate the presence of numerous low mode resonances in a densely spaced range of ratios of net cylinder height to radius in close conformance with linear inviscid theory. Where geometry permits simple corner reflexion, characteristic surfaces are revealed which confirm in part the theoretical predictions concerning their scale and form.Detailed measurements are given of the amplitude at one point within the cylinder for the condition in which the disturbance frequency equals the rotation frequency. Amplitude column height spectra are compared with theoretical estimates, and the evolution of amplitude for the simplest mode of resonant oscillation is studied. A non-linear theory based on the integral energy of large amplitude oscillation is derived whose broad features are in fair quantitative and qualitative agreement with these observations.Some investigation is made of the phenomenon ofresonant collapse, in which larger amplitude resonant oscillations, after persisting in an apparently laminar form, degenerate abruptly into a state of agitation and disorder from which they do not recover. It is found that the time for emergence of this collapse after the introduction of the forcing disturbance has a close correspondence with the theoretical period of one ‘evolutionary’ cycle of momentum exchange between the main motion and the secondary oscillation.