磁耦合式双稳态宽频压电俘能器的设计和俘能特性

为了同时提高振动能量俘获系统的效率和实用性, 俘能器主结构的振动特性与环境振动特性的匹配度显得尤为重要. 非线性系统复杂的动力学行为为设计高效的俘能器奠定了基础, 但结构一旦被设计、生成出来, 其工作频率往往是固定的, 无法根据环境中的振动而发生相应的改变. 本文利用可移动铰支座和非线性磁力设计了一种具有双稳态特性的宽频压电俘能器, 通过拓宽压电俘能器的工作频带, 来匹配环境中较宽的振动频率. 为了保证系统低频宽带的俘能效果, 详细分析了结构的长度比、磁间距、负载阻抗、外激励频率和幅值等对系统线性刚度、非线性刚度以及动力学行为的影响, 并进行了实验验证. 首先将系统简化为欧拉-伯努力梁, 利用拉格朗日方程建立系统的非线性动力学方程, 并利用谐波平衡法进行求解. 针对理论分析给出的不同外激励频率下的最优长度比, 搭建了实验平台进行验证. 理论和实验的结果表明: 非线性磁力的引入使系统呈现负刚度特性, 使俘能器能够在单稳态和双稳态之间的变换, 实现低频俘能效果; 通过调节可移动铰支座的位置, 改变系统的长细比, 能够实现从0到16 Hz的宽频俘能效果. 

DESIGN AND ENERGY CAPTURE CHARACTERISTICS OF MAGNETICALLY COUPLED BISTABLE WIDE BAND PIEZOELECTRIC ENERGY HARVESTER1)

In order to improve the efficiency and practicality of energy harvester simultaneously, the compatibility of the vibration characteristics of the energy harvester and the environment is of utmost importance. The complex dynamic behaviors of nonlinear system lay important foundation for designing efficient energy harvesters. However, once the structures are designed and fabricated, their work frequencies are decided and invariable, and cannot be adjusted to adapt the vibration in environment. A movable hinge support and nonlinear magnetic force are introduced in this paper to design a wide band piezoelectric energy harvester with bistable states. The vibration properties of the designed energy harvester can match with the wide vibration frequencies in environment by widening its working band. In order to make sure the low frequency and wide band energy capture ability, we analyze the influences of structural length ratio, distance between magnets, load impedance, frequency and amplitude of external excitation on the linear stiffness, nonlinear stiffness and dynamic behaviors characteristics of the designed energy harvester system in detailed. Experiments are tested to validate our design and results. Firstly, the designed magnetically coupled bistable wide band piezoelectric energy harvester is simplified as a Euler-Bernoulli beam. Then, the nonlinear dynamic equations of the system are deduced by the Lagrange equation, which can be solved via harmonic balance method. The optical length ratio according to different frequency of external excitation are forecasted theoretically and validated via experimental tests. Numerical and experimental results show that the introduced nonlinear magnetic force makes the system exhibit negative stiffness, which enables the system to switch between monostable and bistable states and finally realize energy capturing in low frequency. What’s more, it can change the length ratio of the designed system by adjusting the location of the movable hinge support, which can make the system capture energy with a wide band from 0 to 16 Hz.