压电自参数吸振-俘能器动力学设计与性能研究

The nonlinear coupling of the piezoelectric autoparametric vibration absorber-harvester is used to control the harmful vibration of its main structure. In the mean time, the piezoelectric effect is utilized to harvest the vibrational energy of the secondary structure for powering the microelectromechanical devices and wireless sensors. As a result, the integration of the vibration control and sensor powering is realized, which has great engineering significances in the mechanical, civil and aerospace fields. In this project, the quadratic coupling between the primary and secondary structures of the piezoelectric autoparametric vibration absorber-harvester is designed based on the principle of nonlinear saturation. A nonlinear distributed-parameter electromechanical-coupled model is established for such a system. Numerical simulations and experimental studies are used to validate the proposed theoretical model. The methods of harmonic balance and multiple scales are then utilized to deduce the closed-form solutions of the responses of the primary and secondary structures and harvested power. The sufficient and necessary condition for the system stability is given by using the Routh-Hurwitz criterion. The forms of motions in the stable and unstable regions are compared. The effects of the parameters, including the external force frequency and amplitude and the load resistance on the stable boundary are analyzed. The nonlinear phenomena such as saturation, jumping and hysteresis are studied. The dynamic design is performed to avoid the unstable movement, such as chaos, by taking advantage of the characteristics of energy harvesting. Considering the synergistic effect of vibration absorption and energy harvesting, the Lagrange multiplier method is used to determine the optimal parameters for improving the performance of the system. Finally, the strategies of the dynamic design and performance enhancement for the piezoelectric autoparametric vibration absorber-harvester are proposed.

通过压电自参数吸振-俘能器非线性耦合对主结构危害振动进行控制，同时利用压电效应采集次结构振动能，为微机电设备和无线传感器供能。实现振动控制-传感供能一体化，在机械、土木、航空航天等领域都具有重大工程意义。本项目首先基于非线性饱和原理设计压电自参数吸振-俘能器主次结构二次耦合作用。为其建立非线性分布参数力电耦合模型，并通过数值仿真和实验研究对理论模型进行验证。然后结合谐波平衡法和多尺度法推导主次结构位移和采集电功率闭合解。采用劳斯-赫尔维茨判据确定压电自参数吸振-俘能器稳定的充分必要条件，对比稳定区与非稳定区的运动形式。分析参数包括外力频率和幅值及负载电阻对稳定边界的影响，研究饱和、跳跃和滞回等非线性现象。进行动力学设计，利用俘能特性规避混沌等不稳定运动。考虑吸振和俘能协同作用，采用拉格朗日乘数法确定系统最优参数，提升系统性能。最终提出压电自参数吸振-俘能器动力学设计和性能提升方案。

通过压电自参数吸振-俘能器非线性耦合对主结构危害振动进行控制，同时利用压电效应采集次结构振动能，为微机电设备和无线传感器供能。实现振动控制-传感供能一体化，在机械、土木、航空航天等领域都具有重大工程意义。本项目考虑压电自参数器件悬臂梁的非线性几何大变形，建立压电自参数器件的力电耦合分布参数模型。为研究其非线性特性，采用等效结构法和多尺度法得到近似解析解。通过实验数据，验证了压电自参数器件的力电耦合分布参数模型近似解析解。解析解揭示了两种类型的运动：零梁变形（梁和基础结构的刚体运动）和非零梁变形（梁和基础结构之间的非线性相互作用）。对于非零梁变形情况，基础结构发生非线性饱和，振动得到有效抑制。给出了系统稳定边界。从稳定区域越过稳定边界到不稳定区域的中心，系统的运动依次经历周期运动、非周期运动和混沌。在不稳定区域，基础结构的控制变得无效。为实现稳定的宽带振动能量采集，提出了一种具有混沌控制功能的自参数内共振压电能量采集器。发现自参数振动能量采集器的混沌特性在引入非线性能量阱的系统中消失。具有非线性能量阱的自参数振动能量采集器的采集带宽度随着激励幅度的增加极大地加宽。非线性能量阱使单位加速度激发的压电自参振动能量采集器的最大平均功率提高了200%。针对智能输电线系统，提出了一种基于内共振的宽带压电吸振-俘能器，有效抑制了输电线路的微风振动，并为在线监测设备供电。

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