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 引用本文: 李琦, 邱志平, 张旭东. 基于二阶摄动法求解区间参数结构动力响应[J]. 力学学报, 2015, 47(1): 147-153.
Li Qi, Qiu Zhiping, Zhang Xudong. SECOND-ORDER PARAMETER PERTURBATION METHOD FOR DYNAMIC STRUCTURES WITH INTERVAL PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 147-153.
 Citation: Li Qi, Qiu Zhiping, Zhang Xudong. SECOND-ORDER PARAMETER PERTURBATION METHOD FOR DYNAMIC STRUCTURES WITH INTERVAL PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 147-153.

SECOND-ORDER PARAMETER PERTURBATION METHOD FOR DYNAMIC STRUCTURES WITH INTERVAL PARAMETERS

• 摘要: 在处理区间参数结构动力响应问题时,现有的分析方法大多局限于一阶区间分析方法. 如果参数的不确定量稍大,采用一阶区间分析方法对结构动力响应范围进行估计可能会失效,所以需要考虑二阶区间分析方法.但是采用基于区间运算的二阶区间分析方法得到的结果将会对动力响应范围过分高估. 为了克服以上缺点,首先基于二阶摄动法得到结构动力响应广义函数. 然后通过求解此动力响应函数的最大和最小值,将结构动力响应区间的问题转化为序列低维箱型约束下的二次规划问题. 最后采用DC 算法(di erence of convex functionsalgorithm) 对这些箱型约束下的二次规划问题进行求解. 这样可以在不引入过多计算量的情况下,避免了对动力响应范围的过分估计. 通过数值算例,将该方法和其他区间分析方法进行比较,验证了该方法的有效性与精确性.

Abstract: When considering the problem of the dynamic responses of structures with interval parameters, previous interval analysis methods are mostly restricted to its first-order. But if the uncertainties of the parameters are fairly large, the response region obtained using the first-order interval analysis method would fail to contain the real region of the dynamic response of uncertain structures. Therefore, the second-order analysis method should be considered. However, the second-order analysis method relating to operations of interval may result in an exorbitantly overestimated dynamic response region, which makes the result useless for practical engineering problems. To circumvent this drawback, firstly the general function of the dynamic response of structures in terms of structural parameters is obtained based on the second-order parameter perturbation method. Then via solving the maximum and minimum of the function, the problem of determining the bounds of the dynamic response of uncertain structures is changed into a series of low dimensional box constrained quadratic problems, and these box constrained quadratic programming problems can be solved using the DC algorithm (difference of convex functions algorithm) effectively. The proposed method can avoid the exorbitant overestimate of the dynamic response region of uncertain structures, while does not introduce much more computational expense. A numerical example is used to illustrate the accuracy and the efficiency of the proposed method when comparing with other methods.

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