The focus of this dissertation is on the dynamics of electromagnetic systems for energy harvesting and filtering applications. The inclusion of magnets into systems generates nonlinearity due to the nature of electromagnetic interactions. In this work, magnetic nonlinearity manifests in tip interactions for cantilever beams, coupling effects for electromagnetic transduction, and bistable potential wells for a two beam system. These electromagnetic interactions are used to add non-contact coupling effects for the creation of bistable oscillators or arrays of coupled beams for energy filtering.
Nonlinearity at the tip of cantilever beams acts to change the dynamic and static behavior of the system. In this dissertation, these interactions are analyzed both with and without the nonlinear tip interactions. A linear analysis of the system without the tip interaction first provides insight into the shifting frequencies of the first four natural oscillation modes when considering a rigid body tip mass with rotational inertia and a center of mass that is offset from the tip of the beam. Then, the characterization of the nonlinearities in the beam stiffness and magnetic interaction provide insight into the static and dynamic behavior of the beam. The analytical and numerical investigations, using Rayleigh-Ritz methods and an assumed static deflection, are shown to be consistent with experimental tests. These methods provide a framework for theoretically establishing nonlinear static modes and small-amplitude linear modes that are consistent with physical behavior.
In electromagnetic coupling, the role of nonlinearity can have a detrimental or beneficial effect on energy harvesting. This work includes an investigation of the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. The system;;s response behavior with linear coupling or a physically motivated form of nonlinear coupling is compared with single and multi-frequency base excitation. This analysis is performed with combined theoretical and numerical studies.
The ability of magnets to add nonlinearity to a system allows for the expansion of the phenomenological behavior of said system and potential advantages and disadvantages for energy harvesting. This work studies a two beam system made up of carbon fiber cantilever beams and attached magnetic tip masses with a focus on energy harvesting potential. Numerical and experimental investigations reveal an array of phenomena from static bifurcations, chaotic oscillations, and sub-harmonic orbits. These features are used to highlight the harvesting prospects for a similarly coupled system.
Beyond nonlinearity, the non-contacting coupling effects of magnets allow for the hypothetical creation of energy filtering systems. In this work, the band structure of a two dimensional lattice of oscillating beams with magnetic tip masses is explored. The focus of the wave propagation analysis is primarily on regions in the band structure where propagation does not occur for the infinite construction of the system. These band gaps are created in this system of 2 x 2 repeating unit cells by periodically varying the mass properties and, for certain configurations, the frequency band gaps manifest in different size and band location. Uncertainty in these regions is analyzed using potential variations associated with specific physical parameters in order to elucidate their influence on the band gap regions. Boundary effects and damping are also investigated for a finite-dimensional array, revealing an erosion of band gaps that could limit the expected functionality.
