单自由度干摩擦振子1:4强共振时的N-S分岔  

N-S Bifurcation of an Oscillator With Dry Friction in 1:4 Strong Resonance

作　　者：郭勇[1] 谢建华[1] 

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《应用数学和力学》2013年第1期18-26,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11172246);中央高校基本科研业务费专题资助项目(SWJ-TU11ZT15)

摘　　要：研究一个单自由度干摩擦系统的受迫振动行为.在1:4共振条件下,根据平衡点附近级数形式的解建立系统的Poincaré映射.运用范式理论将映射简化成标准形式.结果显示,系统会发生NS(Neimark-Sacker)分岔.数值模拟验证了理论结果.An oscillator with dry friction under external excitation was considered. The Poincar6 map was established according to the series solution near equilibrium in the 1：4 reso- nance case. By theory of normal forms, the map was reduced into its normal form. It is shown that there exist phenomena of N-S bifurcations. The theoretical results are verified by numerical simulations.

关 键 词：干摩擦 POINCARÉ映射 共振 范式 周期解 环面 

分 类 号：O322[理学—一般力学与力学基础]