非线性粘弹性杆纵向激励下的混沌行为  

Chaotic Behavior of Nonlinear Viscoelastic Straight Bar During Longitudinal Vibration

作　　者：赵平花[1] 崔艳[2] 王龙飞[2] 

机构地区：[1]太原理工大学体育学院,山西太原030024 [2]太原理工大学力学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2016年第3期245-251,共7页Journal of North University of China(Natural Science Edition)

摘　　要：本文基于Melnikov法对非线性粘弹性杆纵向激励下的动力学行为进行研究.首先,利用RitzGalerkin原理将杆纵振时的动力控制方程转化为非线性微分方程—Duffing振子方程;然后,通过Melnikov函数得到系统进入混沌的阈值.为了研究外部激励与混沌运动之间的关系,进行了一系列的数值计算,得到了以外激振幅为分岔参数的分岔图、X-T关系曲线图、X-X相平面图、庞加莱映射图以及对应的功率谱,从而具体描述了系统的动力学行为.研究表明:非线性粘弹性杆在纵振时由定常运动通过倍周期分岔进入到了混沌运动,其本构方程中的二次非线性项对系统的非线性动力响应影响较大;系统的混沌阈值随外激振幅的不断增大而逐渐减小.Dynamic motion of nonlinear viscoelastic straight bar during longitudinal vibration was investi- gated based on the method of Melnikov. The dynamic governing equation of bar during longitudinal vi- bration was changed into differential dynamic system-Dulling oscillator equation by Ritz-Galerkin princi- ple. By the Melnikov function, chaotic threshold of the system was given. The influences of external loading frequency upon chaotic motion were analyzed by numerical calculation and the motion behavior of system was described through the bifurcation diagrams which bifurcation parameter was amplitude, the time-history curve, phase portrait, Poincare map and power spectrum. The results were given as fol- lows. Steady motion of the system of nonlinear viscoelastic straight bar during longitudinal vibration may be translated into chaotic motion through period doubling bifurcation and the quadric nonlinear item in constitutive relation had great effect on the dynamic behavior. The chaotic threshold value of the sys- tem would decrease with increase of external loading frequency.

关 键 词：粘弹性直杆 纵向激励 Melnikov法 同宿轨道 混沌运动 

分 类 号：O322[理学—一般力学与力学基础]