【作者】 王康；

【导师】 李欣业；

【作者基本信息】 河北工业大学 ， 力学， 2019， 硕士

【摘要】 无线传感器、移动电子设备等的广泛运用,推动了振动能量采集技术的迅猛发展。这一长效能源获取技术在军事装备、野外监测及智能领域都拥有广泛的应用前景以及巨大的潜在商业价值,因此,如何充分发挥采集器的设计潜能、提高能量转化效率,自然成为国内外振动领域学者研究的热点和前沿课题。本文针对弹性支撑下具有双稳态的压电悬臂梁能量俘获系统的动力学行为进行研究。首先基于能引发双稳态现象的磁力模型,利用牛顿第二定律以及基尔霍夫第一定律建立了基础作简谐运动时系统的数学模型。其次根据无量纲化后的控制方程,利用罗斯-霍尔维茨判据分析了平衡点的静态分岔,并通过非线性势函数分析解释了双稳态现象。此外还利用Matlab数值仿真得出压电悬臂梁位移以及输出电压随系统参数和激励参数的变化规律,基于庞加莱映射得到了压电悬臂梁位移和输出电压关于系统参数和激励参数的分岔图。通过多尺度法推导了双稳态压电能量采集系统的平均方程,并根据平均方程定常解存在的条件给出了系统的幅频特性方程。基于幅频特性方程通过同伦延拓法对系统参数和外激励参数做了相关分析,同时基于幅频特性方程对系统压电悬臂梁的振幅做了在不同参数组合下的三维图。1.计算结果表明,无论是数值计算还是用多尺度法进行摄动分析,系统的幅频特性均呈现为硬特性,但压电悬臂梁的振幅随质量比及刚度比的变化却呈软特性,即在某些参数范围内,系统的简谐周期响应发生分岔并导致混沌运动,系统的运动既可以发生在零平衡点附近,也可以发生在非零平衡点附近,甚至是在不同的平衡点之间作大幅跃迁。2.数值分析的结果表明,相同参数下,系统处于双稳态相对单稳态时具有更显著的非线性特性,引入双稳态明显提高了系统的电压输出和响应频带,与线性系统相比较的结果显示,非线性磁力的引入明显提高了系统的电压输出。3.三维图分析的结果表明,当考虑内共振时,系统处于单稳态时压电悬臂梁的振幅相对双稳态时要大,通过压电悬臂梁的振幅随着不同系统参数与外激励参数的变化规律,为能量采集器的设计提供了理论指导,即不管系统处于单稳态还是双稳态,都应选择较低的质量比和较高的刚度比进行参数组合。更多还原

【Abstract】 The wide application of wireless sensors and mobile electronic devices have greatly promoted the development of vibration energy harvesting technology.This long-term energy harvesting technology has broad application prospects and huge potential commercial value in military equipment,field monitoring and intelligence.Therefore,it has naturally became a hot topic and frontier research for scholars in the field of vibration in China and abroad to fully use the potential value of the design and improve the energy conversion efficiency.In this paper,the dynamic behavior of a piezoelectric cantilever energy harvesting system with bi-stable state under elastic support is studied.Based on the magnetic force model which can induce bi-stable phenomena,the mathematical model of the system with two degree of freedom under harmonic base motion is firstly established using Newton’s second law and Kirchhoff’s law.By the Routh-Hurwitz criterion,the static bifurcation of equilibrium point is secondly analyzed after reducing the dimensionless governing equations as state equations with five dimension,and the bi-stable phenomenon is explained by the nonlinear potential function analysis.In addition,the variation of how the displacement and the output voltage of the piezoelectric cantilever beam changes with the system parameters and excitation parameters are obtained by using Matlab numerical simulation,and the distribution of the displacement and output voltage of the piezoelectric cantilever beam with respect to the system parameters and excitation parameters is obtained based on the Poincaré mapping.The averaging equation of the bi-stable piezoelectric energy harvesting system is derived by the method of multiple scales,and the amplitude-frequency characteristic equation of the system is given according to the existence condition of the average equation.Based on the amplitude-frequency characteristic equation,the system parameters and external excitation parameters are analyzed by homotopy continuation method.At the same time,the three-dimensional diagram is made under different parameter combinations based on the amplitude-frequency characteristic equation.1.Both the numerical and analytical results show that the amplitude-frequency curves of the system are in hard characteristic.However the variation of the amplitude of piezoelectric cantilever beam with mass and stiffness ratio are in soft characteristic.From time histories and phase trajectories,the harmonic response of the system may bifurcate,which can lead to complex periodic motion or quasi-periodic motion,even chaotic motion when the parameters of the system are changed.The motion of the system can take place near the zero or non-zero equilibrium point,even jump with large amplitude between the two non-zero equilibrium points.2.What ’ s more,under the same parameters,the system has more significant nonlinear characteristics in the bi-stable compared with mono-stable state,and the application of bi-stable system significantly improved the voltage output and response frequency band of the system,and compared with the linear system,results show that the introduction of nonlinear magnetic force significantly increases the voltage output of the system.3.The results of the three-dimensional graph analysis show that when considering the internal resonance,the amplitude of the piezoelectric cantilever beam is larger than that of the bi-stable state when the system is mono-stable,and the amplitude of the piezoelectric cantilever beam varies with different system parameters and external excitation parameters.The change provides theoretical guidance for the design of the energy harvester,that is,whether the system at in mono-stable state or bi-stable state,the lower mass ratio and higher stiffness ratio should be selected for parameter combination.The results of the numerical analysis agree well with the approximate results obtained by the the method of multiple scales.更多还原