Coupled vibration and parameter sensitivity analysis of rocking-mass vibrating gyroscopes

Vibrating beam gyroscopes are widely used to measure the angle or the rate of rotation of many mechanical systems. The vibration and parameters sensitivity analyses of a specific type of vibrating beam gyroscope namely rocking-mass gyroscopes are presented in this paper. These types of gyroscopes by far have a better performance than the conventional single-beam gyroscopes. The system comprises of four slender beams attached to a rigid substrate, undergoing coupled flexural and torsional vibrations with a finite mass attached in the middle. Two of the beams carry piezoelectric patch actuators on top, while the other two possess piezoelectric patch sensors. Using extended Hamiltonʹs principle, the resulting eight coupled partial differential equations of motion with their corresponding boundary conditions are derived. In spite of the need for a high computational power, the system is analysed in the frequency domain using an exact method and the closed-form characteristic equations for two cases of fixed and rotating base support are obtained. Furthermore, a detailed parameter sensitivity analysis is carried out to determine the effects of different parameters on the complex natural frequencies of the system. Results presented are valuable in the design of this type of gyroscope as the exact resonant conditions and the sensitivity of the system parameters play important roles in the dynamic performance of gyroscopes.