双线性双滞后环系统的约束分岔

吴志强; 张振华; 郝颖

doi:10.7498/aps.60.120503

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.

关键词:

双线性 /
滞后 /
约束分岔

Abstract

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.

Keywords:

作者及机构信息

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

基金项目: 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)和天津市自然科学基金重点项目(批准号:09JCZDJC26800)资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;

2.
Department of Mechanical and Electrical Engineering, Nanyang Institute of Technology, Nanyang 473004, China

参考文献

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施引文献

[1]	Zhang W, Hu H Y 2009 New Development of Nonlinear Dynamic Theory and Applications (Beijing: Science Press) p142 (in Chinese)[张伟、胡海岩 2009 非线性动力学理论和应用的新进展 (北京:科学出版社) 第142页]
[2]
[3]	Li G J, Xu W, Wang L, Feng J Q 2008 Acta Phys. Sin. 57 2107 (in Chinese)[李高杰、徐伟、王亮、冯进钤 2008 57 2107]
[4]	Li S H, Yang S P 2006 J. Dynam. Contr. 4 8 (in Chinese) [李韶华、杨绍普 2006 动力学与控制学报 4 8]
[5]
[6]	Wu Z Q, Yu P, Wang K Q 2004 Int. J. Bifur. Chaos 14 2825
[7]
[8]	Chen Z, Wu Z Q, Yu P 2005 J. Sound Vib. 284 783
[9]
[10]	Huang C T, Kuo S Y 2006 Int. J. Nonlin. Mech. 41 888
[11]
[12]
[13]	Fragiacomo M, Rajgelj S, Cimadom F 2003 Earthq. Eng. Struct. Dyn. 32 1333
[14]	Katsaras C P, Panagiotakos T B, Kolias B 2008 Earthq. Eng. Struct. Dyn. 37 557
[15]
[16]	Christopoulos C 2004 J. Eng. Mech. ASCE 130 894
[17]
[18]	Lau S M L, Lau K T, Yin Y S, Li L, Wong M, Chan K, Chen W 2010 Mater. Manuf. Process. 25 281
[19]
[20]
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[22]	Rustighi E, Brennan M J, Mace B R 2005 Smart Mater. Struct. 4 19
[23]
[24]	Chou C C, Tsai K C, Yang W C 2009 Earthq. Eng. Struct. Dyn. 38 403
[25]
[26]	Stanton J F, Stone W C, Cheok G S 1997 PCI J. 42 20
[27]
[28]	Priestley M J N, Sritharan S, Conley J R, Pampanin S 1999 PCI J. 44 42
[29]
[30]
[31]	Christopoulos C, Tremblay R, Kim H J, Lacerte M 2008 J. Struct. Eng. ASCE 134 96
[32]
[33]	Li H G, Zhang J W, Wen B C 2002 Mech. Res. Commun. 29 283
[34]
[35]	Motahari S A, Ghassemieh M 2007 Eng. Struct. 29 904

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