Size-dependent performance of microgyroscopes

The size-dependent dynamical performance of a microgyroscope is investigated via use of the modified couple stress theory. The size-dependent potential energy and the kinetic energy of the system are constructed as functions of both transverse and lateral motions as well as base-rotation; the works of DC and AC voltages applied by the drive and sense electrodes are constructed in terms of the system parameters. The work and energy terms are balanced via use of Hamilton's principle yielding the continuous expressions for the transverse and lateral motions of the microgyroscope. By means of a weighted-residual method, a reduction procedure is applied leading to a reduced-order model. This model is solved via use of a continuation technique. The relation between the base-rotation and gyroscopic couplings is obtained and the calibration curve of the microgyroscope is plotted. The size-dependent frequency-response curves for the sense and drive directions are obtained; the gyroscopic effect gives rise to the displacement in the sense direction. The effect of different system parameter including the length-scale parameter on the dynamical performance of the microgyroscope is highlighted.