层合圆板俘能器非线性振动的理论与实验研究

Vibration energy harvesting is one of the important power sources of wireless sensor nodes and other micro-electromechanical devices. The laminated circular plate harvester is an essential design configuration in the field of vibration energy harvesters. This project focuses on the nonlinear vibration of the laminated circular plate harvester in theory and experiment. Geometric nonlinearities of the structures, physical nonlinearities of the adhesives and constitutive relationships of piezoelectric materials are all taken into considered establishing the continuum model of the laminated circular plate. Considering the step effect on the surface of the laminated circular plate, the continuum model of the step laminated circular plate harvester is established by using the boundary continuity condition as the link. By means of equation truncation, the descending order model is obtained, and a strong nonlinear approximate analytical method is developed to reveal the influence mechanism of structural parameters on the nonlinear response of the laminated circular plate harvester. A nonparametric identification approach of nonlinear piezoelectric mechanical systems is developed. The experimental model of the laminated circular plate harvester is established by mapping the system restoring force based on the experimental data. The results of theoretical modeling and analytical analysis are verified by the experiment. The theoretical nonlinear model and the experimental technology the laminated circular plate harvester are developed and improved through the researches of this project. It has important scientific and engineering significance in the design and structure optimization of the laminated circular plate harvester.

振动能量俘获是无线传感节点等微机电设备自主供能的重要方法之一，层合圆板俘能器是振动能量俘获领域重要的设计构型。本项目针对层合圆板俘能器的非线性振动开展理论与实验研究，考虑圆板结构的几何非线性、粘接剂的物理非线性和压电材料的本构关系，建立平面层合圆板的连续体模型，分析结构参数对平面层合圆板模态和振型的影响。考虑层合圆板俘能器表面的阶梯效应，以边界连续性条件为纽带，建立阶梯层合圆板俘能器的连续体模型。通过方程截断，得到降阶模型，利用和发展强非线性近似解析方法，明确结构参数对层合圆板俘能器非线性响应的影响机理。提出一种压电俘能器的非参数辨识方法，构建系统恢复力数据映射关系，基于实验数据建立层合圆板俘能器的实验模型，并验证理论建模与解析分析的结果。通过本项目的研究，建立和发展层合圆板俘能器的非线性模型与实验技术，为层合圆板俘能器的设计和结构优化奠定理论基础，具有重要的科学和工程意义。

本项目完成拟定的研究目标，研究层合圆板俘能器的非线性建模和实验验证问题。建立了压电-金属阶梯多层压电圆板的横向振动模型，在考虑中心质量的情况下建立了阶梯层合圆板俘能器的连续体模型。利用谐波平衡方法，分析了层压电圆板振动能量采集器的幅频响应，揭示结构参数对层合圆板俘能器非线性响应的影响机理。提出一种压电俘能器的辨识方法，完成层合圆板俘能器的实验建模。在理论分析、数值仿真和实验研究基础上，验证所建立模型的准确性。研究了基于层合圆板俘能器的轨道噪声能量采集系统，建立了Helmholtz共鸣器的理论模型，得出了共鸣器的谐振频率和声压放大倍数与几何结构尺寸得关系。对轨道噪声能量采集系统进行了理论建模、数值计算和有限元仿真，最后进行了实验验证。