双线性双滞后环系统的约束分岔  

Constrained bifurcations of the system with double-loop bilinear hysteresis

作　　者：吴志强[1] 张振华[1,2] 郝颖[1] 

机构地区：[1]天津大学机械工程学院,天津300072 [2]南阳理工学院机电工程系,南阳473004

出　　处：《物理学报》2011年第12期66-73,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10872142;10472078);教育部新世纪优秀人才支持计划(批准号:NCET-15-0247);高等学校博士学科点专项科研基金(批准号:2009003211005);天津市自然科学基金重点项目(批准号:09JCZDJC26800)资助的课题~~

摘　　要：含双滞后环力-位移关系的系统在工程中有增多的趋势,但相关的动力学研究还较少.以形状记忆合金减振系统为背景,研究了双线性双滞后环系统的主共振分岔问题.首先用平均法求得了正弦激励下系统主共振幅频响应方程.然后利用非光滑系统的约束分岔理论,讨论了环境温度和外激励幅值变化对幅频响应曲线的影响.结果表明:环境温度和外激励幅值组成的参数平面可分成11个区域,每个区域对应一种定性不同的幅频响应解.此外,为便于幅频响应图的描述和比较,提出了一种编码规则来描述响应在扫频时的跳跃现象.这对于系统频响模式的设计具有直接的指导作用.Systems with double-loop hysteresis are used increasingly in engineering,but few studies on their dynamics are reported.In this study,the bifurcation characteristics of the primary resonance of a system with double-loop bilinear hysteresis are investigated on the background of a shape memory alloy damper.First,the frequency-amplitude response equation is obtained by using the averaging methods.Then,the influences of the temperature and the amplitude of excitation on amplitude-frequency responses are analyzed by the constrained bifurcation singularity analysis method of non-smooth systems.The calculation results show that the parameter space composed of the temperature and the amplitude of excitation can be divided into 11 regions,which suggest that there are 11 qualitatively different kinds of amplitude-frequency responses to the variation of two parameters.In order to describe and compare the frequency-amplitude response curves conveniently,an encoding rule is proposed to describe their jump phenomena as the frequency sweeps.The above results can guide directly the design of frequency response mode of the system.

关 键 词：双线性 滞后 约束分岔 

分 类 号：O322[理学—一般力学与力学基础]