| Duffing系统解的转迁集的解析表达式 |
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| 引用本文： | 毕勤胜,陈予恕.Duffing系统解的转迁集的解析表达式[J].力学学报,1997,29(5):573-581. |
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| 作者姓名： | 毕勤胜 陈予恕 |
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| 作者单位： | 天津大学力学与工程测试系 |
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| 基金项目： | 国家自然科学基金,博士点基金 |
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| 摘 要： | 通过对非线性Ｄｕｆｉｎｇ方程解的稳定性进行研究，得到了其周期一解失稳的转迁集的解析表达式，同时应用广义牛顿法，得到了Ｄｕｆｉｎｇ方程对称破缺分岔转迁集的解析表达式，与Ｕｅｄａ用模拟计算机的方法和Ａ．Ｙ．Ｔ．Ｌｅｕｎｇ用增量谐波平衡数值方法的结果吻合良好，克服了用模拟计算机或数字计算机确定物理参数平面上的转迁集计算工作量十分大的困难．
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| 关 键 词： | 转迁集 非线性振动 稳定性 Duffing系统解 |
ANALYTICAL EXPRESSION OF TRANSITION BOUNDARIES OF THE SOLUTION OF DUFFING SYSTEMS |
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| Bi Qinsheng,Chen Yushu.ANALYTICAL EXPRESSION OF TRANSITION BOUNDARIES OF THE SOLUTION OF DUFFING SYSTEMS[J].chinese journal of theoretical and applied mechanics,1997,29(5):573-581. |
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| Authors: | Bi Qinsheng Chen Yushu |
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| Abstract: | The nonlinear Duffing equation is studied and fold boundaries of period T are obtained by introducing Burton's and Cheung's results and nonlinear frequency. Also, the transition boundaries of symmetric breaking are obtained by general Newton's method. Our results are in good agreement with Leung's by IHB method,and we overcome the difficulty of great quantities of computation by computer. |
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| Keywords: | nonlinear frequency fold boundary of period T symmetric breaking transition boundary |
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