Duffing振子双稳态压电悬臂梁俘能器的分析与设计

发布时间：2018-01-22 14:49

本文关键词： Duffing振子双稳态压电悬臂梁混沌振动激励阱间跳跃频率比俘能　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：环境能量收集技术是当前热点的研究课题之一,其中双稳态压电悬臂梁振动俘能器由于其结构简单而备受关注。但目前关于混沌振动能量的俘获技术的研究却没有公开报道。然而,混沌振动是介于周期振动和随机振动之间的另外一种特殊振动形式。因此,对安装在混沌振子上的俘能器进行研究和设计具有一定的理论和实际应用意义。本文研究了安装在Duffing振子上的双稳态压电悬臂梁俘能器的相关问题,包括俘能器对振子混沌运动的影响,俘能器在混沌振动激励下的俘能机理以及Duffing振子双稳态压电悬臂梁俘能器的优化设计等。研究表明,对于混沌振动激励,广泛应用的平均输出功率并不能全面地衡量俘能效果,本文从储能的角度提出阱间跳跃频率比这一衡量俘能效果的指标作为衡量俘能效果的补充。本文具体的研究内容和相关结论如下:1.运用牛顿第二定律建立了 Duffing振子的动力学方程,分析了外界激励频率和幅值变化时振子的振动特性。考虑俘能器悬臂梁的质量分布,将其视为欧拉-伯努利梁,将加装于振子上的悬臂梁俘能器与振子视为一个两自由度系统,运用Language方程建立系统的耦合动力学方程和机电耦合方程,并进一步分析了加装悬臂梁之后振子的混沌特性。发现俘能器的加装并不会对振子的混沌振动产生影响,将此混沌振动作为俘能器的输入激励,发现悬臂梁只会出现混沌运动,而不会出现周期运动。2.对双稳态俘能器的俘能机理进行的深入的研究。分析了目前常用的衡量俘能效果指标的不足,并从储能的角度提出了阱间跳跃频率比这一衡量俘能效果的指标。研究表明悬臂梁阱间跳跃频率比越大,越有利于储能。3.以全局最大平均输出功率和阱间跳跃频率比超过95%为优化设计目标,采用蒙特卡罗方法,确定出俘能器磁铁间距和负载电阻的最优取值组合。所提出的优化设计方法既能实现电能的最大化转化,又能最大程度地将该电能储存。本文的研究为混沌振子双稳态压电悬臂梁俘能器的设计提供了理论依据和方法,对拓宽俘能器的应用具有一定的参考价值。
[Abstract]:Environmental energy collection technology is one of the hot research topics. Among them, bistable piezoelectric cantilever vibration energy capture device has attracted much attention because of its simple structure. However, the research on chaotic vibration energy capture technology has not been reported publicly. Chaotic vibration is another special form of vibration between periodic vibration and random vibration. The research and design of the energy capture installed on the chaotic oscillator has certain theoretical and practical significance. In this paper, the related problems of the bistable piezoelectric cantilever energy capture installed on the Duffing oscillator are studied. . It includes the effect of energy capture on chaotic motion of vibrator, the mechanism of energy capture under chaotic vibration, and the optimization design of Duffing vibrator bistable piezoelectric cantilever beam energy capture. For chaotic vibration excitation, the average output power can not be used to measure the energy capture effect. In this paper, from the perspective of energy storage, the hopping frequency ratio between wells is proposed as a complement to the measurement of capture energy effect. The specific research contents and relevant conclusions are as follows:. 1. The dynamic equations of Duffing oscillator are established by using Newton's second law. The vibration characteristics of the vibrator are analyzed when the external excitation frequency and amplitude change. Considering the mass distribution of the cantilever beam of the energy capture device, it is regarded as an Euler-Bernoulli beam. The cantilever beam energy capture and oscillator are regarded as a two-degree-of-freedom system. The coupling dynamic equations and electromechanical coupling equations of the system are established by using the Language equation. The chaotic characteristics of the vibrator with cantilever beam are further analyzed. It is found that the addition of the energy capture does not affect the chaotic vibration of the vibrator, and the chaotic vibration is regarded as the input excitation of the vibrator. It is found that the cantilever beam will only appear chaotic motion, but not periodic motion. 2. The mechanism of capture energy of bistable energy capture device is studied deeply. The deficiency of the commonly used indexes to measure capture energy effect is analyzed. From the point of view of energy storage, the index of hopping frequency ratio between wells is proposed to measure the energy capture effect. The study shows that the greater the jump frequency ratio between cantilever beams is, the higher the hopping frequency ratio is. The more favorable energy storage. 3. With the global maximum average output power and hopping frequency ratio more than 95% as the optimization design goal, the Monte Carlo method is used. The optimal combination of magnet spacing and load resistance is determined. The proposed optimization design method can realize the maximum conversion of electric energy. The research in this paper provides a theoretical basis and method for the design of a bistable piezoelectric cantilever energy holder for chaotic oscillators, and has a certain reference value for widening the application of the energy capture device.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM619

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