受参数激励屈曲梁的次谐分岔和混沌运动  

Subharmonic Bifurcations and Chaos of the Buckled Beam Subjected to Parametrical Excitations

作　　者：张冬梅 李锋 Zhang Dongmei;Li Feng(School of Mathematics and Statistics,Linyi University,Linyi 276000,China)

机构地区：[1]临沂大学数学与统计学院,临沂276000

出　　处：《数学理论与应用》2022年第2期25-34,共10页Mathematical Theory and Applications

基　　金：National Natural Science Foundation of China(Nos.11902133,12071198);Natural Science Foundation of Shandong Province(No.ZR2018MA016)。

摘　　要：本文研究受参数激励屈曲梁的次谐分岔和混沌行为,得到系统混沌和非混沌区域的临界曲线,给出系统发生次谐分岔和混沌的条件,并证明有限次的次谐分岔可以激发混沌运动.同时,通过数值模拟,给出系统的相图、庞加莱截面图和最大李雅普诺夫指数,并验证我们的理论分析结果.In this paper the subharmonic bifurcations and chaotic motions of the buckled beam model subjected to parametric and additive excitations are investigated.The critical curves separating the chaotic and non-chaotic regions are obtained,the conditions of subharmonic bifurcations and chaos are given,and it is showed that the system may be chaotically excited by finite subharmonic bifurcations.Furthermore,numerical simulations are used to obtain the phase portraits,the Poincare sections and the maximal Lyapunov exponents and to verify our theoretical analysis results.

关 键 词：屈曲梁 次谐分岔 混沌 MELNIKOV方法 

分 类 号：O342[理学—固体力学]