期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Stability Analysis of an Autoparametric Vibration System
摘要/Abstract
摘要：
研究了一类带有粘性阻尼摆的自参数振动系统.通过系统运动的拉格朗日方程和牛顿第二定律,建立了振动系统的运动方程;采用多尺度法寻找方程的二阶近似解;讨论其平衡解,并通过罗斯-霍尔维兹判据判断其稳定性条件;数值模拟了系统的幅频响应曲线和Poincaré映射图.
Abstract：
The complex dynamic behavior of the autoparametric vibration system with an attached damped pendulum is studied.The dynamical equation of the system is established using Lagrangian and Newton's second law.The multiple scale method is employed to look for the second order approximate solutions of the equation.The balanced solution is discussed,and then stability conditions of the equilibrium solution are judged by Routh-Hurwitz criterion.Numerical simulations of the amplitude-frequency response curve and Poincaré sections are performed.
关键词
关键词：
自参数振动系统
;
多尺度法
;
稳定性
;
Poincaré映射图
Key words：
autoparametric vibration system
;
multiple scale method
;
stability
;
Poincaré sections