三自由度双侧刚性约束振动系统的概周期运动  

QUASI-PERIODIC MOTIONS OF A THREE-DEGREE-OF-FREEDOM VIBRATING SYSTEM WITH TWO RIGID CONSTRAINS

作　　者：张艳龙[1] 王丽[2] 

机构地区：[1]兰州交通大学机电工程学院,甘肃兰州730070 [2]兰州城市学院数学系,甘肃兰州730070

出　　处：《工程力学》2009年第2期71-77,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10572055;50475109);甘肃省自然科学基金项目(3ZS062-B25-007;3ZS042-B25-044)

摘　　要：通过模态矩阵法解耦,建立了一类具有双侧刚性约束的三自由度冲击振动系统的对称型周期运动及Poincaré映射,研究了系统映射在其Jacobian矩阵的一对复共轭特征值穿越复平面单位圆周情况下的概周期运动,并通过数值仿真揭示了系统在弱共振条件和三种强共振条件下的概周期运动及其经锁相或环面倍化通向混沌的转迁途径,给出了系统从概周期运动变成混沌运动激振频率的变化范围。With the help of an uncoupled approach of modal matrices, the symmetrical periodic motion and Poincare mapping of a three-degree-of-freedom vibrating system with two rigid constrains are derived analytically. Quasi-periodic motions of the system are investigated by concerning one complex conjugate pair of eigenvalues passing through a unit circle in Jacobian matrix. In non-resonance case and three strong resonance cases, quasi-periodic motions of symmetrical periodic motions and their routes to chaos via lock phase or torus doubling are also illustrated by numerical simulation. And the excited-frequency range from quasi-periodic motions to chaotic motions of the system is obtained.

关 键 词：冲击振动 映射 周期运动 共振 混沌 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]