Abstract
Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems. In this paper, the Melnikov theory is introduced to overcome it. Firstly, the Melnikov state-space model of the nonlinear piezoelectric vibration energy harvesting (PVEH) system is built. Based on it, chaotic dynamics mechanisms of achieving broadband PVEH by nonlinearity are exposed by potential function of the unperturbed nonlinear PVEH system. Then the corresponding Melnikov function of the nonlinear PVEH system is defined, based on which two Melnikov necessary conditions of determining the distance are obtained. Finally, numerical simulations are done to testify the theoretic results. The results demonstrate that the distance is closely related to the excitation amplitude and frequency once geometric and material parameters are fixed. Under a single-frequency excitation, the nonlinear PVEH system can generate a periodic vibration around a stable point, a large-amplitude vibration around two stable points, or a chaotic vibration. The proposed method is very valuable for optimally designing and utilizing nonlinear broadband PVEH devices in engineering applications.
Highlights
Nowadays, Internet of Things (IoTs) is a research and application hot spot, which can allow objects to be sensed and controlled remotely across existing network infrastructure
Advances in low power design open the possibility of harvesting ambient vibration energy to power wireless sensor nodes (WSNs), which is called vibration energy harvesting including electrostatic [1], electromagnetic [2], and piezoelectric mechanisms [3]
Piezoelectric mechanisms are of particular interest due to their high energy densities, no electromagnetic inference, and integration potential, which is always called piezoelectric vibration energy harvesting (PVEH)
Summary
Internet of Things (IoTs) is a research and application hot spot, which can allow objects to be sensed and controlled remotely across existing network infrastructure. For a given PVEH structure, theoretical analysis is done to demonstrate its nonlinearity and experiments are done to validate its broadband characteristics Among all studies, it is the most easy and common way to construct nonlinear PVEH systems by using magnetic forces [13,14,15,16,17]. The Melnikov theory provides a unified framework for studying transitions and chaos in a wide class of deterministic and stochastic nonlinear planar dynamic systems with restoring forces. It can be used to find necessary conditions for homoclinic bifurcations to occur in multiwell systems [18] This is the same case as nonlinear PVEH systems where restoring forces come from electromechanical coupling force and nonlinear magnetic force. The goal of this paper is to build necessary conditions of determining a proper distance between two magnets based on the Melnikov method.
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