一种弹性支撑双稳态压电能量俘获系统的动力学仿真分析

Dynamical simulations of a bi-stable piezoelectric energy harvesting system with elastic support

为了揭示双稳态能量俘获系统的复杂动力学行为及现象,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。最后,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和分岔图。结果表明,系统的幅频特性呈现为硬特性,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。因此,相同参数下,系统具有双稳态时比单稳态时具有更丰富的运动形式,可明显提高系统的电压输出和响应频带。研究结果可为工程实际中如何优化振动能量采集器提供理论依据。

The dynamic behavior of a piezoelectric cantilever energy harvesting system with bi-stable state under elastic support is studied to reveal its complex phenomena.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 by using Newton's second law and Kirchhoff′s law.By the Routh-Hurwitz criterion,the static bifurcation of equilibrium points,is secondly analyzed for the dimensionless governing equations.At last,the amplitude variations of the displacement of piezoelectric cantilever beam and the variations of the output voltage with the system parameters and excitation parameters and their bifurcation diagrams are obtained by Matlab numerical simulations.The results show that the amplitude-frequency curves of the system are in hard characteristic,while the amplitude variations of the displacement of piezoelectric cantilever beam with mass ratio and stiffness ratio are in soft characteristic.That is,within some parameters intervals,the harmonic response of the system has bifurcation and leads to chaotic motion.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.For the same parameters,bi-stable systems have richer forms of motion compared to mono-stable ones,and significantly increase voltage output and response frequency band of the system.The research result may provide theoretical reference for how to optimize vibration energy collector in practice.