摘要
为得到基底简谐激励下带光滑立方刚度非线性能量阱的强调制反应必要条件及充分条件,利用复变量平均法推导了慢变系统方程.慢不变流形的相轨迹分析表明,激励幅值满足折奇点条件才可能出现强调制反应,但也可能吸引至某一慢不变流形的稳定分支.算例分析证实:当慢变系统响应超越慢不变流形上极值点幅值,又不吸引至慢不变流形某一分支,并且形成连续跳跃环路而不陷入局部循环时,强调制反应才出现.所推得的慢变系统微分方程计算数值与实际模拟值基本吻合,而慢变系统的数值曲线相对简单,易于分辨且计算方便.
With the complex-averaging method,a slow dynamics system for nonlinear energy sinks(NES)system with purely cubic stiffness under ground harmonic excitation was formulated to gain the necessary condition and sufficient condition of strongly modulated response(SMR).Analysis of the phase portrait of the slow invariant manifold(SIM)shows that SMR appears when the excitation amplitude meets the condition of folded singularity,whereas it may be attracted to certain stable branches of SIM.The case study and discussion show that the SMR should exist if the response of the slow dynamics system surpass the extreme value of the SIM;however,it has not attracted to the stable branches of SIM and can also form the continuous closed loops without any local circles.Theoretical analysis of the slow dynamics system agrees with real numerical simulation results.It is relatively simple and easy to identify for numerical curves of slow dynamics system as well as convenient calculation.
作者
刘良坤
谭平
陈洋洋
闫维明
周福霖
LIU Liangkun;TAN Ping;CHEN Yangyang;YAN Weiming;ZHOU Fulin(College of Architecture and Civil Engineering,Beijing University of Technology,Beijing 100124,China;Earthquake Engineering Research & Test Center,Guangzhou University,Guangzhou 510405,China)
出处
《北京工业大学学报》
CAS
CSCD
北大核心
2019年第2期177-185,共9页
Journal of Beijing University of Technology
基金
国家自然科学基金资助项目(51478129
51408142)
教育部创新团队资助项目(IRT13057)
广东省特支计划资助项目(2014TX01C141)
关键词
复变量平均法
非线性
慢变系统
强调制反应
慢不变流形
complex-averaging method
nonlinear
slow dynamics system
strongly modulated response(SMR)
slow invariant manifold(SIM)
