| 一类强非线性机械基础系统的亚谐振动解析解 |
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| 引用本文： | 鲍文博,闻邦椿.一类强非线性机械基础系统的亚谐振动解析解[J].应用力学学报,2003,20(2):140-144. |
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| 作者姓名： | 鲍文博 闻邦椿 |
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| 作者单位： | 1. 沈阳工业大学,沈阳,110023;东北大学,沈阳,110004
2. 东北大学,沈阳,110004 |
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| 摘 要： | 建立了机械基础动力系统的强非线性动力学模型，利用能量法对该系统的周期解进行了解析研究，确定了系统动态参数满足周期解的条件、系统的周期解以及解的稳定性判别式。发现了亚谐振动，并给出了系统在满足周期解条件下的一组参数对应的主振动、1／3亚谐振动和1／5亚谐振动。最后利用数值积分方法计算了系统在给定条件下的主振动及亚谐振动解，考察了解析解的正确性。
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| 关 键 词： | 机械基础动力系统 强非线性动力学模型 亚谐振动 能量法 周期解 数值积分 |
| 文章编号： | 1000-4939(2003)02-0140-05 |
| 修稿时间： | 2002年1月18日 |
Analytical Periodical Solution of Subharmonic Resonance in a Strongly Nonlinear System of Machine Foundations |
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| Bao Wenbo , Wen Bangchun.Analytical Periodical Solution of Subharmonic Resonance in a Strongly Nonlinear System of Machine Foundations[J].Chinese Journal of Applied Mechanics,2003,20(2):140-144. |
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| Authors: | Bao Wenbo Wen Bangchun |
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| Affiliation: | Bao Wenbo 1,2 Wen Bangchun 2 |
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| Abstract: | A strongly nonlinear dynamicl model of machine foundation system is presented, and the analytical research on the periodic solution of the system is developed using the energy method in this paper. The condition of the periodic solution which must be satisfied by the dynamical parameters, the periodic solution of the system and the discriminant of the stability are suggested. Besides main resonance, the subharmonic resonance in the system is detected, and a set of periodic solution of main and 1/3 & 1/5 subharmonic resonance under the periodic condition are given as examples. Finally the periodic solution of the system is investigated with the numerical method, and the precision of analytical method is compared with numerical one. |
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| Keywords: | machine foundations strong nonlinearity subharmonic resonance |
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