Abstract
The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing, gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realized through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well_oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multi-modal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential.
Highlights
Vibration energy harvesting is a relatively recent concept
Most vibration energy harvesting concepts deal with ambient vibrations acting as translational base excitations for the harvesting attachment [8,9]
The major advantage of nonlinear energy harvesting can be ascertained from the hardening spring influence upon the frequency response curve (FRC), in which an increase occurs in the response bandwidth [25]
Summary
Vibration energy harvesting is a relatively recent concept. Mechanical systems generally experience vibrations due to manufacturing or assembly imperfections [1], transient and impulsive loading [2] and wear/degradation. Despite an overwhelming diversity of proposed concepts and designs, one can identify two major classes of vibration harvesters; cantilever beams with a tip mass in bending mode [10,11,12] (usually coupled with piezoelectric elements), or a base-excited seismic magnetic mass, oscillating in the proximity of an electric coil. The major advantage of nonlinear energy harvesting can be ascertained from the hardening spring influence upon the frequency response curve (FRC), in which an increase occurs in the response bandwidth [25] This effect allows for a broader range of frequencies over which power can be generated efficiently, compared with a linear system. An estimation of the induced load power is provided
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