This research is classified into two broad sections: ring-based MEMS (Micro-electro Mechanical Systems) and macro gyroscopes and novel bi-stable/monostable nonlinear energy harvesting systems. In both cases, models and solution methods are based on ring structural dynamics considering comprehensive nonlinear formulations. The investigation of nonlinear and linear dynamic response behavior of MEMS and macro ring gyroscopes forms the basis of the first study. This class of MEMS/macro ring-based vibratory gyroscopes requires oscillatory nonlinear electrostatic/electromagnetic excitation forces for their operation. The partial differential equations that govern the ring dynamics are reduced to a set of coupled nonlinear ordinary differential equations by assuming nonlinear and linear mode functions and via the application of Galerkin\u27s procedure. Understanding the effects of nonlinear actuator dynamics via suitable modeling is considered essential and adequately addressed. An external excitation of the ring gyroscope at a frequency close to the system resonant frequency is necessary to increase operational sensitivity. The variation of natural frequencies has been examined theoretically and experimentally. Nonlinear and linear dynamic responses in the driving and sensing directions are examined via time responses, phase diagram, Poincareβ map, and bifurcation diagram in the presence of input angular motion and the excitation forces. The second part of this research focuses on the design, modeling, and dynamic analysis of novel macro and MEMS ring energy harvesting systems. This study is concerned with nonlinear dynamic analysis of both bistable and monostable ring structure-based energy-harvesting systems. The ring structural elements in this class of harvesters are considered as an alternative to the previously used beam and tube structural configurations. Comprehensive mathematical models for the proposed nonlinear and linear ring harvester systems and nonlinear magnetic and electrostatic forces that act on the ring structure are formulated. Ambient sinusoidal excitations in a broad range of frequencies are considered as the energy source to the harvester. Consideration of the harvester system nonlinearities and the nonlinear external magnetic force results in system bi-stability and an increased ii frequency range. Also, external excitation of the ring-based nonlinear harvester at a frequency close to the system resonant frequency associated with the second flexural mode is essential to increase operational efficiency. Ring-based bi-stable and monostable broadband energy harvesters are entirely new to the literature and are designed and analyzed in the present study. The time response, phase diagram, Poincare map, and bifurcation diagram when the nonlinear system is subjected to ambient harmonic excitation and a nonlinear magnetic force have been employed to understand the system response and the generated power. These investigations are envisaged to provide an insight into the dynamics of these devices and to aid ongoing research associated with their fabrication as well as future design improvements
