双稳态压电悬臂梁发电系统的动力学建模及分析  

Dynamic modeling and analysis of a bistable piezoelectric cantilever power generation system

作　　者：孙舒[1,2] 曹树谦[1,2] 

机构地区：[1]天津大学机械工程学院,天津300072 [2]天津市非线性动力学与混沌控制重点实验室,天津300072

出　　处：《物理学报》2012年第21期95-106,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11172199)资助的课题~~

摘　　要：针对双稳态压电悬臂梁发电系统进行了动力学建模与分析.首先建立了能引发系统双稳态现象的磁力模型,给出了两磁铁之间磁力的数学表达式;其次建立了压电悬臂梁发电系统的集中参数模型,得到了系统发生双稳态现象时磁铁之间的距离范围;通过数值计算分析了系统的响应特性,发现双稳态运动大大提高了系统的频率响应范围,并且系统在低激励频率和低激励幅值下能发生大幅运动,而激励幅值越大,系统具有越高的能量逃离势阱产生大幅运动;最后通过实验对数值计算结果进行了验证.研究结果为双稳态压电悬臂梁发电系统的设计与应用提供了理论依据.Dynamic modeling and analysis of a bistable piezoelectric cantilever power generation system are presented. Firstly, a magnetic force model is established which could induce bistability, and the force mathematical expression between the two magnets is given. Secondly, a lumped parameter model of piezoelectric cantilever power generation system is built, and the range of distance between the two magnets is analyzed while the bistable phenomenon occurs. Thirdly, the response characteristics of the system are studied numerically. The results show that the beam undergoes large-amplitude motion at low frequency and low amplitude, and that the voltage response has a broadband. The system has high energy escaped from potential well when excitation amplitude imereases. Finally, the result is verified experimentally. This study provides a theoretical basis for the design and application of bistable piezoelectric cantilever power generation system.

关 键 词：双稳态悬臂梁 压电发电 大幅运动 混沌运动 

分 类 号：TM919[电气工程—电力电子与电力传动] O415.5[理学—理论物理]