Parallel solution of upper and lower bounds on eigenvalues for uncertain structures
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摘要: 当工程结构参数包含不确定因素时,结构的固有频率也将是不确定的.这就需要讨论不确定性振动问题中广义区间特征值的求解方法.在Deif标准区间特征值求解定理的基础上,通过区间分析,将特征值的上下界分解成2个广义特征值问题进行求解.基于此求解方法的并行性分析,给出并行求解算法,克服了求解区间问题计算量大的缺点,使传统串行机或者串行算法难以解决的区间特征值问题得以较好的解决.Abstract: When the structure parameter contains uncertain information and uncertain features in the practice engineering, the inherent frequency of the structure is also uncertain. Then the generalized solution method of the interval eigenvalue problem that for the uncertain dynamic structure need to be considered. Based on the Deif′s solution theorem for standard interval eigenvalue problem, and through the interval analysis, the upper and lower bounds of the structure eigenvalues could be transformed into two generalized eigenvalue problems to deal. For avoiding the disadvantages of the interval vertex solution method of the structure eigenvalues, such as large calculation and much runtime of the vertex solution, the parallel algorithm which could be used in largescale computing was presented. Based on the solution of the parallel analysis, it can be concluded that the parallel algorithms can solve many large scale interval problems which can not be resolved by traditional serial algorithm.
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Key words:
- eigenvalue /
- interval analysis method /
- uncertain system /
- parallel algorithm
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