具有记忆特征的振动能量采集系统随机动力学研究

Vibration energy harvesting system, as one of the research hotspots in the field of nonlinear dynamics, can convert the vibration energy in the environment into electrical power, thus providing reliable energy supply for the microelectronic devices. At present, most of the research work focused on the deterministic vibration energy harvesting system, ignoring the stochastic factors and little attention was paid to the vibration energy harvesting system with memory characteristic. The project intends to focus on two kinds of typical vibration energy harvesting system with memory characteristic (time-delayed vibration energy harvesting system and fractional-order vibration energy harvesting system) under random excitations. The main research contents of this project are as follows: Using variable transformation and stochastic averaging method to study the stochastic response and stability of time-delayed vibration energy harvesting system and to explore the influence of time delay on the system response and stability; Put forward efficient numerical algorithm for the fractional-order vibration energy harvesting system under random excitations; The generalized harmonic function and stochastic averaging method are used to study the stochastic response and stability of the fractional-order vibration energy harvesting system under random excitations, and the influence of the fractional derivative term on the output voltage and power is discussed. The completion of this project will provide reliable theoretical support for the optimal design of the vibration energy harvesting system and promote the development of stochastic dynamics.

振动能量采集系统可以将环境中的振动能转化为电能，从而为微电子设备提供可靠的能源供给，是当今非线性动力学领域的研究热点之一。目前绝大部分的成果属于确定性振动能量采集系统的研究，较少考虑随机因素的影响，并且很少关注具有记忆特征的振动能量采集系统。本项目拟以随机激励下两类典型具有记忆特征的振动能量采集系统（时滞振动能量采集系统和分数阶振动能量采集系统）为研究对象，开展其动力学研究。主要内容包括：使用变量代换方法和随机平均法研究随机激励下时滞振动能量采集系统随机响应和稳定性，探讨时滞因素对系统响应和稳定性的影响；提出适用于随机激励下分数阶振动能量采集系统的高效数值方法；使用广义谐和函数和随机平均法研究随机激励下分数阶振动能量采集系统的随机响应和稳定性，讨论分数阶导数项对输出电压和功率的影响。本项目的完成将为振动能量采集系统的优化设计提供可靠的理论基础，推动随机动力学学科的发展。

振动能量采集技术因其在众多领域的巨大应用潜能，引起了广泛的关注。随机激励在现实的环境中是广泛存在的，会影响系统的动力学行为。在过去的三年里，我们主要聚焦研究几类随机激励下具有记忆特征的振动能量采集系统的动力学行为，这几类系统分别为时滞振动能量采集系统，分数阶振动能量采集系统和粘弹振动能量采集系统。结合随机平均法，广义谐和函数，多尺度方法和非光滑变换方法等，我们初步建立了一套研究上述几类系统随机响应和随机分岔的理论分析方法。数值结果也表明我们提出的方法是有效的。我们还发展了逐步稀疏回归方法，可以实现基于状态数据的混合式能量采集系统的建模。在项目的支持下，我们在国内外知名期刊发表了12篇SCI论文，这些期刊为《Mechanical Systems and Signal Processing》、《International Journal of Non-Linear Mechanics》、《European Physical Journal Plus》、《Nonlinear Dynamics》、《International Journal of Bifurcation and Chaos》、《Chaos Solitons & Fractals》、《Chaos》、《Acta Mechanica Sinica》、《Chinese Physics B》、《IEEE Access》和《Machines》。