随机双稳态压电振动能量采集系统的动力学与控制

Piezoelectric energy harvesting system is currently one of the most active research fields, due to its advantages of good mechanical-electrical conversion efficiency and prone to micromation. To clarify the influence of nonlinearity and complex stochastic factors are very important. This project aims at applying foundational researches for stochastic bistable piezoelectric vibration energy harvesting system, establish the theories and numerical simulation methods of nonlinear dynamics, and explain the influence of nonlinearity on energy harvesting system from global perspective; develop the analytical and numerical methods for piezoelectric energy harvesting system under noise excitation; establish and solve the FPK equation; investigate stochastic bifurcation, stochastic resonance and stochastic chaos of the system under harmonic and noise excitations; elucidate the Influence mechanism of the noise intensity on frequency width and output voltage; by applying the orthogonal polynomial approximation method, research the stochastic dynamic behavior and its evolution of piezoelectric energy harvesting system under the influence of random parameters. Finally, propose the stochastic control strategy and system structure optimization to improve the efficiency of energy harvesting system. The objective of this project is to build up the scientific analytical and numerical methods for bistable piezoelectric vibration energy harvesting system under the impact of stochastic factors initially, to promote the development of stochastic dynamics and to provide theoretical basis for the researches and applications of energy harvesting field.

压电振动能量采集系统因力电转换性能好、易微型化等优点，其研究已成为当今科学前沿与热点之一，阐明非线性和复杂随机因素对系统的影响至关重要。本项目拟针对随机双稳态压电振动能量采集系统展开应用基础研究，建立双稳态压电振动能量采集系统的非线性动力学全局分析理论和数值方法，阐释非线性对系统能量转换的影响；进一步发展噪声激励下此类系统的解析方法与数值算法，建立并求解系统的FPK方程，探索谐和激励和噪声作用下系统的随机分岔、随机共振以及随机混沌等动力学现象，阐明噪声对扩宽系统工作频率和提高输出电压的作用机理；发展随机参数影响下系统的正交多项式逼近方法，讨论参数的随机性对系统动力学行为及其演变的影响机制；最后，提出随机控制策略、构建系统结构优化方案，以提升发电效率。初步建立一套随机因素影响下双稳态压电振动能量采集系统的分析理论和数值方法，促进随机动力学学科的发展，为能量采集方向的研究与应用提供理论依据。

本项目针对多种非线性能量采集系统，开展了如下一些主要研究：1.对复杂噪声激励下压电能量采集系统进行了响应分析，通过理论分析和数值模拟相结合的方法研究了能量采集系统的动力学响应，利用电压的时间历程图和均方电压的变化趋势分析并对比了碰撞和各参数对系统能量采集效率的影响，为优化能量采集性能提供参考。2.对具有粘弹性阻尼的非线性能量采集系统进行了动力学分析，采用随机平均法推导出位移与速度的稳态概率密度函数，并讨论了噪声强度、分数阶导数、分数阶阻尼系数等对于非线性能量采集器输出功率的影响。将理论结果与数值模拟结果进行比较，验证了分析结果的有效性。3.针对具有随机参数的参激Duffing系统和三稳态能量采集系统，首先对其复杂动力学行为进行分析，明确其动力学行为的发生、发展和变化规律；随后，基于正交多项式逼近理论，将随机系统转化为高维等效确定性系统，通过对等效确定性系统的探究，分析了随机参数对Duffing系统和三稳态压电能量采集系统的作用机理，揭示了不确定参数对能量采集性能的影响。4.研究了受时滞反馈控制下的非线性压电能量采集系统的动力学行为。基于标准随机平均法得到了振动幅值、位移、速度的稳态概率密度以及均方电压的近似表达式。同时考虑了加性与乘性激励强度、反馈强度、时滞等系统参数对于均方电压的影响。揭示了在随机激励下，时滞反馈控制对该系统的优化效果。