惯容式宽带能量采集技术：随机分析与实验研究

“Inerter”represents the mechanical equivalent of a capacitor, using the force-current analogy between mechanical and electrical networks. As the extension of the traditional mass, the structure and its mechanical behavior of the inerter have been sufficiently studied. The inerter has an incomparable advantage in the passive vibration suppression of the vehicle and has been preliminarily applied to the vibration energy harvesting technique. So far, the vibration energy harvesting technique based on inerter is limited to the linear system under deterministic excitation. Although the linear system has high energy collection efficiency under certain excitation frequency, the efficiency of broadband excitation is significantly reduced. This project study the inerter-type broadband vibration energy harvesting technique, establish electro-mechanical coupling equations of nonlinear energy harvesting system, develop the analytical and semi-analytical techniques for random response, reveal influences of the system parameters on the energy harvesting efficiency; give the reasonable description of the non-smoothness in the inerter, develop the techniques of dealing with the non-smoothness in random system, discuss the influences of non-smooth factors on the energy harvesting efficiency; Finally, the effectiveness and precision of the proposed technique are verified by experiments. This research will lay the foundation for the application of the inerter in broadband energy harvesting technique, and in theory the techniques of dealing with the nonlinear non-smooth random systems are developed.

通过力学元件与电学元件类比创造的惯容器是对传统质量概念的推广，其构造及自身之力学行为已得到深入研究。惯容器在运载工具的被动振动抑制方面具有无与伦比的优势，并已被初步应用于振动能量采集技术。迄今，基于惯容器的振动能量采集技术仅限于研究确定性激励下的线性体系。线性体系尽管在特定的激励频率下具有高的能量收集效率，但对宽带激励情形效率显著下降。本项目研究惯容式宽带振动能量采集技术，建立非线性采集系统之机电耦合方程组，发展其随机响应的解析及半解析分析技术，揭示能量采集效率对各重要参量的依赖关系；建立惯容器本身所具有的强非光滑因素的合理描述方式，发展随机系统中非光滑因素的合理处理技术，探讨非光滑因素对能量采集效率的影响；最后，通过实验技术验证上述分析技术的有效性和精度。本项目将为惯容器在宽带振动能量采集技术中的应用奠定基础，并将在理论上发展非光滑随机系统的响应分析技术。

本项目研究主要内容是各系统参数对惯容式宽带能量采集系统的能量采集效率的影响。研究成果如下：（1）通过分析惯容式旋转电磁能量转换结构，建立了其力学物理模型，研究表明该结构同时具有惯性和阻尼耦合效应。该结构的惯性效应可显著降低结构的固有频率，而其阻尼效应则等效于粘性阻尼；（2）分析了惯容式电磁能量采集装置对瞬态随机激励的响应，揭示各种旋转电磁能量转换结构参数对能量采集效率的影响规律，如旋转惯性有碍于能量采集；（3）通过引入等效线性化方法，分析了齿轮-齿条间的摩擦对其性能的影响，并比较了库伦摩擦模型和粘-滑模型的不同动力学特性，同时验证了等效线性化方法对瞬态响应分析的有效性；（4）通过引入两自由度动力学系统，增加了系统响应带宽，并研究了系统参数对其性能的影响规律。研究结果表明，两个线性弹性系数之间存在着某种最优组合，需要同时调整系统刚度，而旋转结构的附加质量效应仍具有负效应；（5）分析了系统的刚度非线性效应。不同于确定性激励，刚度非线性对应系统随机响应具有不利影响。同时表明，刚度非线性的存在显著改变了系统的动力学特性。通过调整系统刚度等参数，发现了概率密度函数的峰值可由单峰向多峰改变，发生了随机P-分叉行为。通过本项目的研究，揭示了惯容式宽带能量采集系统在随机载荷作用下的动力学特性，厘清了各种影响参数对其工作效率的作用机制，为设计和优化随机载荷下惯容式宽带能量采集系统奠定了理论基础。