Static deflection and pull-in instability analysis of differential-frequency microgyroscopes made of axially functionally graded graphene material

In recent years, graphene platelet (GPL) has attracted extensive attention due to its excellent material properties. However, in the field of rotating microstructures, the potential of GPL has not been fully explored. This paper introduces a design for an electrostatically actuated vibrating beam microgyroscope incorporating GPL, which has the unique feature that the GPL gradient varies along the axial direction rather than only along the thickness direction as in the traditional case. This research involves five different distribution patterns of GPL: UD, AFG-A, AFG-V, AFG-X and AFG-O. In these distribution patterns, the Young's modulus and mass density change dynamically along the axial displacement, which has a significant impact on the vibration characteristics of the microgyroscope. In order to accurately capture the dynamic behavior of this system, this paper uses the extended Hamilton's principle to obtain the governing equations of the vibrating beam microgyroscope, and employs the Galerkin method to discretize the partial differential equations into ordinary differential equations. By considering different distribution patterns and geometric parameters, the static deformation, pull-in voltage and natural frequency of the microgyroscopes were studied. The rotation of the base will cause the frequency of the system to split in half, so the frequency difference method can be used to detect its rotational angular velocity. It is found that the different distribution patterns can significantly change the vibration performance and sensitivity of vibration beam microgyroscopes. In addition, this paper also studied the influence of GPL weight fraction on the performance of the vibrating beam microgyroscope. The study found that a small amount of GPL can significantly improve the sensitivity of the device. © 2025 Elsevier Ltd