## 留言板

 引用本文: 陈塑寰, 郭睿, 孟广伟. 多参数结构特征二阶灵敏度[J]. 应用数学和力学, 2009, 30(12): 1387-1398.
CHEN Su-huan, GUO Rui, MENG Guang-wei. Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1387-1398. doi: 10.3879/j.issn.1000-0887.2009.12.001
 Citation: CHEN Su-huan, GUO Rui, MENG Guang-wei. Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1387-1398.

• 中图分类号: O327

## Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

• 摘要: 提出了一种有效计算多参数结构特征值与特征向量二阶灵敏度矩阵——Hessian矩阵的方法．将特征值和特征向量二阶摄动法转变为多参数形式，推导出二阶摄动灵敏度矩阵，由此得到特征值和特征向量的二阶估计式．该法解决了无法用直接求导法计算特征值和特征向量二阶灵敏度矩阵的问题．数值算例说明了该算法的应用和计算精度．
•  [1] Fox R L,Kapoor M P. Rates of change of eigenvalues and eigenvectors[J]. AIAA Journal，1968，6(12)：2426-2429. doi: 10.2514/3.5008 [2] Nelson R B. Simplified calculations of eigenvector derivative[J]. AIAA Journal，1976，14(9)：1201-1205. doi: 10.2514/3.7211 [3] Juang J N, Ghaemmaghami P,Lim K B. Eigenvalue and eigenvector derivatives of a nondefective matrix[J]. Journal of Guidance, Control Dynamics，1989，12(4)：480-486. doi: 10.2514/3.20435 [4] Lee I W,Jung G H. An efficient algebraic method for computation of natural frequency and mode shape sensitivities[KG*5]. —part Ⅰ distinct natural frequencies[J]. Computers and Structures，1997，62(3)：429-435. [5] Lee I W,Jung G H. An efficient algebraic method for computation of natural frequency and mode shape sensitivities[KG*5]. —part Ⅱ multiple natural frequencies[J].Computers and Structures，1997，62(3)：437-443. [6] Lim K B,Junkins J L. Re-examination of eigenvector derivative[J]. Journal of Guidance，1987，10(6)：581-587. doi: 10.2514/3.20259 [7] Liu Z S, Chen S H,Zhao Y Q.An accurate method for computing eigenvector derivatives for free-free structures[J]. Computers and Structures，1994，52(6)：1135-1143. [8] Moon Y J, Kim B W, Ko M G,et al.Modified modal methods for calculating eigenpair sensitivity of asymmetric damped system[J]. International Journal for Numerical Methods in Engineering，2004，60(11)：1847-1860. doi: 10.1002/nme.1025 [9] Gong Y L,Xu L. Sensitivity analysis of steel moment frame accounting for geometric and material nonlinearity[J].Computers and Structures,2006，84(7)：462-475. [10] Maddulapalli A K, Azarm S,Boyars A. Sensitivity analysis for product design selection with an implicit value function[J]. European Journal of Operation Research，2007，180(3)：1245-1259. [11] Choi K M,Jo H K, Kim W H,et al.Sensitivity analysis of non-conservative eigensystems[J].Journal of Sound and Vibration，2004，274(3/5)：997-1011. [12] Chen S H. Matrix Perturbation Theory in Structural Dynamic Design[M].Beijing：Science Press,2007. [13] Liu X L. Accurate modal perturbation in non-self-adjoint eigenvalue problem[J]. Communications in Numerical Methods in Engineering，2001，17(10)：715-725. doi: 10.1002/cnm.443 [14] Godoy A, Taroco E O,Feijoo R A.Second-order sensitivity analysis in vibration and buckling problems[J]. International Journal for Numerical Methods in Engineering，1994，37(23)：3999-4014. [15] Mirzaeifar R, Bahai H, Aryana F,et al.Optimization of the dynamic characteristics of composite plates using an inverse approach[J].Journal of Composite Materials，2007，41(26)：3091-3108. [16] Mirzaeifar R, Bahai H,Shahab S.Active control of natural frequencies of FGM plates by poezoelectric sensor/actuator pairs[J].Smart Materials and Structures，2008，17(4), 045003.doi: 10.1088/0964-1726/17/4/045003. [17] Mirzaeifar R, Bahai H,Shahab S.A new method for finding the first- and second-order eigenderivatives of asymmetric non-conservative systems with application to an FGM plate actively controlled by piezoelectric sensor/actuators[J]. International Journal for Numerical Methods in Engineering，2008，75(12)：1492-1510. doi: 10.1002/nme.2308 [18] Aryana F,Bahai H. Sensitivity analysis and modification of structural dynamic characteristics using second order approximation[J]. Engineering Structures，2003，25(10)：1279-1287. [19] Bahai H, Farahani K,Djoudi M S. Eigenvalue inverse formulation for optimizing vibratory behavior of truss and continuous structures[J]. Computers and Structures，2002，80(27/30)：2397-2403. [20] Farahani K,Bahai H. An inverse strategy for relocation of eigenfrequencies in structural design—part Ⅱ second order approximate solutions[J]. Journal of Sound and Vibration，2004，274(3/5)：507-528. [21] Choi K M, Cho S W, Ko M G,et al.Higher order eigensensitivity analysis of damped systems with repeated eigenvalues[J]. Computers and Structures，2004，82(1)：63-69. [22] Guedria N, Chouchane M,Smaoui H.Second-order eigensensitivity analysis of asymmetric damped systems using Nelson’s method[J].Journal of Sound and Vibration，2007，300(3/5)：974-992.

##### 计量
• 文章访问数:  1332
• HTML全文浏览量:  95
• PDF下载量:  942
• 被引次数: 0
##### 出版历程
• 收稿日期:  2009-02-17
• 修回日期:  2009-10-15
• 刊出日期:  2009-12-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈