| 不确定非线性结构动力响应的区间分析方法 |
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| 引用本文： | 邱志平,马丽红,王晓军.不确定非线性结构动力响应的区间分析方法[J].力学学报,2006,38(5):645-651. |
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| 作者姓名： | 邱志平 马丽红 王晓军 |
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| 作者单位： | 北京航空航天大学 固体力学研究所 |
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| 基金项目： | 国家杰出青年科学基金（10425208）,国家自然科学基金委与中国工程物理研究院联合基金（10376002）资助项目. |
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| 摘 要： | 研究多自由度非线性不确定参数系统的动力响应问题. 以区间数学为基础，将不确定
性参数用区间进行定量化，借助一阶Taylor级数，给出了近似估计非线性振动系统动力响
应范围的区间分析方法. 从数学证明和数值算例两方面，将其与概率摄动有限元法进行了比
较，结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点.
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| 关 键 词： | 动力响应 非线性振动系统 区间分析方法 概率摄动有限元法 不确定参数 |
| 文章编号： | 0459-1879（2006）05-0645-07 |
| 收稿时间： | 2005-07-21 |
| 修稿时间： | 2006-04-10 |
Interval analysis method for response analysis of nonlinear vibration systems with uncertain parameters |
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| Qiu Zhiping,Ma Lihong,Wang Xiaojun.Interval analysis method for response analysis of nonlinear vibration systems with uncertain parameters[J].chinese journal of theoretical and applied mechanics,2006,38(5):645-651. |
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| Authors: | Qiu Zhiping Ma Lihong Wang Xiaojun |
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| Institution: | Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China |
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| Abstract: | Dynamic response of the MDOF nonlinear vibration system with parameters of uncertainty is studied. Based on interval mathematics, with the parameters of uncertainty being modelled as interval numbers, a new method is proposed to approximately estimate the nonlinear dynamic response range with the help of first-order Taylor series. Comparisons between the interval analysis and the probability perturbation finite element method are made with respect to the mathematical proof and numerical examples, and the advantages of the presented method are shown, including less prior information being required for parameters of uncertainty and higher accuracy. |
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| Keywords: | dynamic response nonlinear vibration finite element method parameters of uncertainty system interval analysis method probability perturbation |
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