The objective of this paper is to present a novel nonlocal strain gradient formulation for dynamic analysis of microgyroscopes. Taking into account the effect of nonlocal and gradient strains, the coupled equations of motion and the corresponding boundary conditions are derived using the Hamilton’s principle. Reduced order models for electrostatic and electrodynamic performance of the gyroscope are presented based on Galerkin projection technique. First, the influence of nonlocal and length-scale parameters on the electrostatic instability of the microgyroscope are investigated and it will be demonstrated that for electrostatic loading, the pull-in instability is delayed with decreasing the nonlocal and/or increasing the length-scale parameters. Then the equations governing the electrodynamic performance of the system are solved and the time responses and phase diagrams along to the drive and sense directions are presented. The stable amplitude and instability margin of the gyroscope under electrodynamic loading will be demonstrated to be subjected to nonlocal and lengthscale parameters. Finally the frequency response of the gyroscope along the sense and drive directions are scrutinized. Accordingly, it will be shown that the nonlocal and length-scale values affect the near-resonance amplitude of vibration significantly. Furthermore, altering the values of nonlocal and length-scale parameters can change the distance between two peak frequencies as well as their absolute values.

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