摘 要

目前，能源问题越来越严重，在世界范围内都引起了极大关注。在当今社会，电能的获取大多数都通过电网和蓄电池来实现，但是电池容量往往不能满足要求，这就只能通过利用风能、太阳能、环境振动能等环境能量来发电才能解决电能供应问题。随着低功耗电子设备迅速发展和社会对新能源的迫切需求，越来越多的学者已经把能量收集系统视为一个重要的研究领域，而压电能量收集器凭借其寿命长、无污染，能量收集便易等优势，使其成为研究热点。但是大多数国内外基于压电能量收集器的研究都是传统的线性收集器，而非线性能量收集器却没有得到很成熟的研究，然而对于传统的线性能量收集器，非线性具有更宽的工作频带，更高的输出性能等特点。本文将基于传统的悬臂梁式能量收集器通过引入磁力（非线性力）来研究非线性能量收集器的结构设计并通过仿真分析来得到输出特性。

本文的工作概括如下：1）首先参考了众多文献期刊等并选取了一系列最合理的数据作为研究的原始依据。这其中主要是悬臂梁与压电片的参数，分为建模参数和结构参数；2）再根据压电悬臂梁的受力情况建立了电悬臂梁的机电耦合集中参数模型，结合原始建模参数利用simulink建立了线性压电能量收集器的数学模型。并生成了线性状态下的振动位移时域图和电压输出时域图，之后改变simulink里模块的参数可以得到不同的输出曲线达到仿真的效果。3）然后在模型基础上引入非线性磁力，再整合磁力公式得到完整的数学模型。利用MATLAB对其进行编程建模并仿真，并将确定的参数函数化对其进行仿真结果分析以得出各参数对输出特性的影响达到优化的目的。通过分析得到了频域图，相图，时域图，势阱图，线性与非线性带宽比较图等等。其中对于压电片的设计是基于参考文献的资料确定一组最契合的数据，再保证压电基底不变，改变压电片的尺寸大小，来仿真分析，最终确定最优的压电片尺寸的。

关键词：压电，能量收集，非线性，集总参数模型；

Abstract

At present, the energy problem has become more and more serious, which has aroused great concern in the world.In today's society, the obtaining of electric energy is to achieve by most of the power grids and the battery , but the battery capacity often can not meet the requirements, this can only be achieved by using wind energy, solar energy, environmental vibration energy environment energy to generate electricity in order to solve the power supply problem.With the low power consumption electronic equipment rapidly development and social on new energy urgent demand, more and more scholars have energy collection system is an important research field, and pressure energy collector by virtue of its long life, no pollution, energy harvesting and easy to use and other advantages, and make it become the research hot spot.But most at home and abroad based on the research of electric energy collector pressure is the traditional linear collector, and nonlinear energy collector has not been very mature, however for the traditional linear energy collector, nonlinear with wider band, higher output performance characteristics.In this paper, based on the traditional cantilever beam type energy collector, the structure design of nonlinear energy collector is studied by introducing magnetic force (nonlinear force), and the output characteristics are obtained through simulation analysis.

The work of this paper is summarized as follows:1) first of all, a series of the most reasonable data are selected as the original basis of the research. The parameters of the cantilever and the piezoelectric plate are mainly divided into the modeling parameters and the structural parameters;2)According to the force of the cantilever beam, the electromechanical coupling lumped parameter model is established, and the mathematical model of linear piezoelectric energy collector is established by using Simulink. And generates the linear state of the vibration displacement of the time domain and the voltage output of the time domain diagram, after changing the parameters of the Simulink module can get different output curves to achieve the simulation results;3) Then, the nonlinear magnetic force is introduced into the model, and then the integrated magnetic force formula is used to get the complete mathematical model. MATLAB is used to program the modeling and simulation, and the parameter function is determined. The simulation results are analyzed to obtain the effect of the parameters on the output characteristics to achieve the purpose of optimization. Through the analysis of the frequency domain diagram, phase diagram, time domain diagram, potential well diagram, linear and nonlinear bandwidth comparison chart, etc.One for the design of piezoelectric patches is determined based on the references, a group of the most fit to data, to ensure that a piezoelectric substrate constant, change the size of the piezoelectric patches, simulation and analysis, ultimately determine the optimal piezoelectric patch size.

Keywords: piezoelectric, energy collection, nonlinear, lumped parameter model