| 张淼,于澜,鞠伟.亏损振系广义状态向量灵敏度的移频算法[J].计算力学学报,2013,30(6):872~878 |
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| 亏损振系广义状态向量灵敏度的移频算法 |
| Moving-frequency algorithm of generalized eigenvetor sensitivity for defective dynamic system |
| 投稿时间：2012-10-09 修订日期：2012-12-17 |
| DOI：10.7511/jslx201306020 |
| 中文关键词: 亏损系统 广义状态向量 灵敏度分析 移频 全模态算法 |
| 英文关键词:defective system generalized eigenvector sensitivity analysis moving frequency full-mode algorithm |
| 基金项目:吉林省自然科学基金（201215115）资助项目. |
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| 中文摘要: |
| 由于亏损系统的状态向量系线性相关，故无法实现与非亏损系统类似的解耦及控制，这为亏损系统灵敏度分析带来很大困难。针对这个问题本文摒弃一般状态向量系，首先引入广义状态向量及其伴随向量理论，利用它们具有的良好规范正交关系，实现了灵敏度控制方程解耦，其次使用移频技术，实现了亏损系统状态矩阵的广义状态向量的灵敏度分析。该方法可用于求解亏损系统各频段广义特征向量的灵敏度，算法结构紧凑，易于理解和实施。数值算例结果表明，该算法是可行和有效的。 |
| 英文摘要: |
| The difficulty of sensitivity analysis of defective system lies in the degenerate eigenspace whose eigenvectors are not orthogonal and linearly independent ones,hence the eigenspace does not possess a linearly independent basis associated with the general eigenspace.We found a set of new generalized eigenvectors associated with the Jordan eigen-equations,which can form orthogonal properties with its corresponding vectors,and introduced a technology of moving frequency.So the controlled equations of sensitivity coefficients are decoupled and the sensitivity coefficients can be obtained.The approach presented here will shed much light on the problem of sensitivity for generalized eigenvectors in all frequency domains.The algorithm is brief and rapid; its treatment is preformed easily.A numerical example is provided to illustrate the accuracy and efficiency of the algorithm. |
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