This paper investigates the dynamic behaviour of a rotating ring that forms an essential element in ring-based vibratory gyroscopes that utilize oscillatory electromagnetic forces. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electromagnetic force that acts on the ring structure is formulated. In order to predict the dynamic behaviour of a ring system subjected to external excitation and body rotation, discretized equations obtained via Galerkin’s procedure is employed to investigate the time as well as frequency response behavior. Dynamic response in the driving and the sensing directions are examined via time responses, phase diagram, Poincare’ map and bifurcation plots when the input angular motion and the nonlinear electromagnetic force are considered simultaneously. The analysis is envisaged to aid ongoing experimental research as well as for providing design improvements in Ring-based Gyroscopes.

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This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

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This paper aims to focus on the design and analysis of a novel ring-based mono-stable energy-harvesting device that is considered as an alternative to the beam and tube models used thus far. The highly sensitive ring second flexural mode, when combined with the nonlinear external magnetic force, results in an ideal combination that yields increased frequency range, and can be considered as novel in the field of vibration-based energy harvesters. A mathematical model for the ring structure, as well as a model to generate nonlinear magnetic force that acts on the ring structure, is formulated. The discretized form of the governing equations is shown to represent a Duffing oscillator in the presence of an external magnetic field. The forms of the system potential energy, as well as the restoring force, are examined to ensure that the mono-stable behavior exists in the proposed model. Numerical predictions of time response, frequency response, phase diagram, and bifurcations map when the system is subjected to ambient harmonic excitation, have been performed for the purposes of gaining an insight into the dynamics and power generation of this new class of harvesters.