Nonlinear Analysis Of A Piezoelectric Energy Harvester

During the last decade, as a promising technology for wireless applications, energy harvesting from ambient waste energy for the purpose of running low-powered electronics has emerged. Energy harvesters can scavenge energy from environment in micro-electromechanical systems. Energy harvesters have three different types of electromechanical transduction, that is, piezoelectric, electromagnetic and electrostatic, in which piezoelectric energy harvesters draw most attention. The reason is that piezoelectric energy harvesters usually have higher power density and simple structures. The piezoelectric energy harvesters are also investigated in this thesis. In the present work, a typical vibration-based piezoelectric nonlinear energy harvester consisting of two permanent magnets connected by the electric circuit with an electric load is investigated.At first, we investigate the frequency response of the bistale piezoelectric energy harvester under the harmonic excitation. The influence of the change of distance between static and moving magnets on nonlinearity of this system is also investigated. The potential schematic of the piezoelectric cantilever shows the system changes from monostable to bistable when distance between moving magnet and static magnet decreases. The distance between moving and static magnetic is the tuning parameter in this example. Decreasing the distance between moving and static magnetic will make the system transform from linear type to nonlinear type. Under the linear conditions, we obtain the typical resonance lines of the piezoelectric energy harvester. With decreasing the distance between stationary and moving magnets, we find that the frequency range of larger output power is larger than that in the linear zone. In order to investigate nonlinear area, we pay attention to the typical nonlinear energy harvester when △=3mm. Besides available frequency range of energy harvesting increases, we find that potential barrier will prevent moving magnets passing through the equilibrium position when the excitation frequency is relatively small. In this condition, the moving magnet only vibrates around the minimum beam potential position.In present work, we use the integral equation method to solve the periodic solutions of the energy harvesting system for various systems parameters. The integral equation method can be applied in the fields of nonlinear vibration and magnetic hrodynamic self-excitation phenomena , which has good numerical robustness and accuracy. The dimensionless governing equations of the piezoelectric energy harvester are usually used to solve the periodic orbits. They are typical nonlinear second-order differential equation, including the displacement of the moving magnets and voltage coupling equation. The integral equation method can reduce computational difficulty and cost. All the process of applying the integral equation method to derive periodic orbits of piezoelectric energy harvester is given in detail. We also studied the stability of the periodic solutions and the bifurcation phenomenon. In this work, the monodromy matrix is used to judge the stability of periodic orbits. The values of eigenvalues of the monodromy matrix show the stability of periodic orbits. When eigenvalues of the monodromy matrix is larger than 1, the periodic orbits become unstable; when the eigenvalues are smaller than-1, periodic doubling bifurcation appears; when conjugate complex eigenvalues exceed the unit circle, Hopf bifurcation appears. By investigating the stability of periodic orbits under different parameter, we have the conclusion that with larger θ and smaller μc, it is more likely to keep the periodic orbits stable.Our work will be of significance in parameter optimization of the energy harvesters.