一个具有正负刚度的分段线性系统的动力学研究  

Research on a Piecewise Linear Dynamic System with Positive and Negative Stiffness

作　　者：杨淑萍[1] 刘熙娟[1] 陈多花 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《海南师范大学学报（自然科学版）》2015年第3期245-249,共5页Journal of Hainan Normal University（Natural Science）

基　　金：甘肃省国际科技合作计划项目(1104WCGA195)

摘　　要：用数值积分的方法仿真一个具有正负刚度的分段线性振荡系统,得到了该系统在某些参数域中的相图、时域响应图和分岔图.数值分析表明:发生非受迫性振动时,无论从怎样的初值开始,系统最终的运动都趋于稳定的平衡点;发生受迫性振动时,在特定的参数条件下,系统运动趋于稳定的极限环;另外,增大阻尼和激励幅值可以有效地控制系统的混沌行为.A piecewise linear vibration systems with positive and negative stiffness is analyzed by the numerical integration method. Through the numerical analysis,the phase diagrams, time response diagrams and bifurcation diagrams in some parameters domain were obtained. Analysis showed that the oscillation converged to fixed points under all the initial conditions if the oscillator was unforced; As for the forced system,the oscillation converged to a stable limit cycle depending on the given parameters;Damping and excitation amplitude was adequately enough to reduce the chaotic behavior.

关 键 词：分段光滑系统 负刚度 分岔 数值仿真 

分 类 号：O193[理学—数学]