附磁阶梯变厚度悬臂梁压电俘能器的理论建模及分析

论文建立了一种附磁阶梯变厚度压电悬臂梁的动力学模型并分析了系统的俘能特性。基于Euler-Bernoulli梁理论分段建立系统能量函数并引入非线性磁势能，利用Lagrange方程建立了系统机电耦合动力学方程；利用数值方法分析了磁间距对系统振动特性的影响，此外还研究了系统单稳态和双稳态响应，探讨了厚度比、长度比、磁间距和外激励幅值对系统动力学响应和俘能特性的影响。结果表明，磁间距是影响系统势能的主要因素，调节磁间距可使系统产生单稳态和双稳态响应，从而有效提高俘能器俘能特性；与传统等截面悬臂梁压电俘能器相比，通过优化结构参数，附磁阶梯变厚度悬臂梁压电俘能器能够发生明显的非线性振动现象，实现宽频带振动能量采集。

Theoretical modelling and analysis of piezoelectric vibration energy harvester based on stepped variable thicknesses cantilever beam with magnetic force

Vibration energy harvesting can be designed as self-powered devices for low power electronic such as wireless sensor network and wearable electronics. Thus, it have attracted much attention in recent years. In this work, a piezoelectric vibration energy harvester (PVEH) based on stepped variable thicknesses cantilever beam with magnetic force is proposed. First, the nonlinear magnetic force is introduced and the energy functions are obtained by using Euler-Bernoulli beam theory. The Lagrange Equation is applied to establish the coupled electromechanical dynamics equation. Finally, the influence of the distance between two magnets on the vibration characteristics of the system is examined. Moreover, the mono-stable and bi-stable responses are analyzed, and the effects of the distance between two magnets and external excitation amplitude on the vibration and voltage responses are investigated. It can be concluded that the magnets distance is the main factor affecting the potential energy of the system. There can occur monostable and bistable responses by adjusting the magnets distance, thus effectively improving the energy harvesting characteristics of the PVEH. Compared with the traditional piezoelectric energy harvester with constant cross-section cantilever beam, the proposed PVEH with magnetic stepped variable thickness cantilever beam can emerge obvious nonlinear phenomena and achieve broadband frequency responses by optimizing the structural parameters.