Investigation of instability and vibration behavior of microbeam-gyroscope with considering distribution of proof mass

In this research, vibration behavior of a microgyroscope including beam structure is investigated. microgyroscope consists of a microcantilever beam and distributed proof mass that is actuated by electrostatic force. A developed model and formulation based on the distributed assumption for proof mass are presented to investigate the instability and vibration behavior of beam microgyroscope. Considering distributed assumption for proof mass, electrostatic force changes from concentrated force to distributed force and produces a moment that is effective on the mechanical behavior of the gyroscope.The equations of motion are reduced by Galerkin’s method and solved via numerical and analytical techniques. An important nondimensional parameter named as nondimensional length parameter is presented which it is the ratio of the proof mass length to beam length. Effects of the nondimensional length parameter on the static, dynamic, vibration behaviors and natural frequency of the microsyetem are investigated. Results show that by increasing the nondimensional parameter, the differences between the results of concentration and distribution hypothesizes for proof mass increase.