窄带随机激励双稳压电悬臂梁响应机制与能量采集研究

具有中心频率的窄带随机振动是一种典型的环境振动，其振动特征与环境的变化密切相关.本文以双稳压电悬臂梁能量采集系统为研究对象，分析系统在不同磁铁间距下的等效线性固有频率特性，以带通滤波器输出一定带宽的窄带随机激励模拟环境振动，研究系统的响应和能量采集特征.研究表明，对于一定带宽的窄带随机激励，一方面系统始终存在一个固定的磁铁间距使其输出达到峰值，另一方面当激励中心频率在一定范围内变化时，系统还分别存在另外两个或一个不同磁铁间距也能使系统输出达到峰值，而且该峰值特性是系统在其等效线性固有频率处诱导双稳或单稳“共振”形成的.研究结果可为具有窄带随机激励特征的振动能量采集提供一定的理论和技术支持.

Mechanism of a nonlinear bistable piezoelectric cantilever beam under narrow-band random excitations and its energy harvesting

While wireless sensors, data transmission devices and medical implant devices tend to miniaturization and low consumption, energy supply modes such as batteries, solar energy and wind energy are limited due to their defects. Instead, vibration energy harvesting can open up new possibilities for self-supplying the low-consumption devices. The narrow-band random vibration with center frequency is a typical vibration in the environment, and its characteristics are closely related to the environment.
This paper takes the energy harvesting system with bi-stable piezoelectric cantilever beam as a research object, and the characteristics of system's equivalent linear natural frequency, linear and nonlinear stiffness under different intervals between magnets are analyzed. By using the narrow-band random excitation with a certain bandwidth output of the bandpass filter to simulate environment vibration and using Runge-Kutta method to solve the system equation numerically, the response of system and the characteristics of energy harvesting are studied.
It is observed that the variation of the magnet spacings at peak output voltage, which possesses a central frequency, is related to the variation of the equivalent linear natural frequency of the system with the interval between magnets. When the variation of magnet spacing is triggered by the narrow-band random excitation with a certain bandwidth, there is always a constant interval between magnets, making the system produce a peak output, which is like a bi-stable system that produces the peak output at optimal spacing under broad-band excitation. On the other hand, there are also more than one or two different magnet spacings making the system produce peak outputs while excitation's center frequency changes in a certain range, and the peak outputs are formed by bi-stable or single-stable “resonance” of the system, induced at the equivalent linear natural frequency. And the demarcation point spacing of the single-stable and bi-stable vibration of the system are the magnet spacing when linear stiffness is zero.
Therefore, for the narrow-band random excitation in the actual environment, the magnet spacing of the energy harvesting system can be reasonably arranged according to the specific working conditions to achieve better electromechanical energy conversion. The findings in this paper can provide some theoretical and technical support for the study of harvesting the vibration energy with characteristics of narrow-band random excitation.