| 784 | 21 | 17 |
| 下载次数 | 被引频次 | 阅读次数 |
首先提出了一种弹簧摆模型,通过谐波平衡法对弹簧摆的内共振现象进行了解析处理,得到了弹簧摆内共振条件以及X、Z两模态能量之间的转换关系.再利用数值模拟得到弹簧摆内共振时的时序图、相图、轨迹图、能量图以及内共振耦合区域图等,分析表明,解析和数值模拟的结果与实验结果吻合一致.
Abstract：In this paper,we have put forward a sort of spring pendulum model.Through the harmonic balance method,the autoparametric resonance of the spring pendulum has been analytically processed.The condition of the autoparametric resonance of the spring pendulum has been obtained,and the transform relationship between X and Z models has been discussed.Moreover,the graphs of displacement,phase,trajectory,energy and autoparametric resonance area have been numerically obtained.Analyses indicate that the results obtained here agree well with the experimental results.
[1]褚亦清,李翠英.非线性振动分析[M].北京:北京理工大学出版社,1996.975～983
[2]石玉仁,薛具奎.弹簧摆的混沌行为[J].西北师范大学学报,2001:37(3):91～97
[3]司丽荣,张竞夫.弹簧摆内共振现象的实验研究[J].物理实验,2002,22(3):9～12
[4]王建平,刘宏昭,原大宁,苏致霄.一类非线性振动系统改进状态空间模型及其数值方法[J].应用力学学报,2002,19(4):112～116
[5]Cuerno R,Ranada A F,Ruiz-Lorenzo J J.Deter-ministic chaos in the elastic pendulum:A simple laboratory for nonlinear dynamics[J].Am.J.Phys,1992,60(1):73
[6]Davidovic D M,Anicin B A,Babovic V M.The libration lim its of the elastic pendulum[J].Am.J.Phys,1996,64(3):338
[7]王永岩.理论力学[M].北京:科学出版社,2007.428～438
[8]陈树辉.强非线性振动系统的定量分析方法[M].北京:科学出版社,2007.169～174
[9]刘延柱,陈立群.非线性振动[M].北京:高等教育出版社,2001.57～59
[10]朱因远,周纪卿.非线性振动和运动稳定性[M].西安:西安交通大学出版社,1992.32～36
[11]Press W H,Teukolsky S A,Vetterling W T.Numerical Recipes-The Art of Scientific Computing[M].Cambridge,UK:Cambridge University Press,1996
基本信息:
中图分类号:O322
引用信息:
[1]郑建龙,虞献文.弹簧摆的内共振特性分析[J].物理与工程,2010,20(02):13-16.
基金信息:
浙江省科技计划项目(2008C31013);; 金华市科技项目(2006-1-017)
2010-04-15
2010-04-15