多参数结构特征二阶灵敏度

陈塑寰; 郭睿; 孟广伟

doi:10.3879/j.issn.1000-0887.2009.12.001

多参数结构特征二阶灵敏度

doi: 10.3879/j.issn.1000-0887.2009.12.001

1.
吉林大学南岭校区力学系,长春 130025;2.吉林大学南岭校区汽车动态模拟国家重点实验室,长春 130025

基金项目: 吉林省科学技术发展基金资助项目(20070541)

详细信息

作者简介:
陈塑寰(1934- ),男,广东兴宁人,教授(E-mail:chensh@jlu.edu.cn);郭睿(1978- ),女,吉林人,讲师,博士(联系人.Tel:+86-431-8505090;E-mail:guo.rui@ascl.jlu.edu.cn).

中图分类号: O327
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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

Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

1.
College of Mechanical Science and Engineering, Nanling Campus, Jilin University, Changchun 130025, P. R. China;

摘要

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．
- 多参数结构 /
- 二阶特征灵敏度 /
- 有效计算方法
Abstract: A method for computing the second-order sensitivity matrix of eigenvalues and eigenvectors of the multiple parameter structures,i.e.the Hessian matrix,was presented.The second-order perturbations of eigenvalues and eigenvectors were transformed into the multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors were developed.Using these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation were obtained to estimate the changes of eigenvalues and eigenvectors when design parameters changed.The method avoided direct differential operation thus reducing the difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example was given to demonstrate the application and the accuracy of the proposed methods.
- multiple parameter structures /
- second-order sensitivity of eigenpairs /
- efficient computational method

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参考文献(22)

[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. doi: 10.1016/0045-7949(94)90180-5
[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. doi: 10.1016/j.compstruc.2005.10.005
[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. doi: 10.1016/j.ejor.2006.03.055
[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. doi: 10.1016/S0022-460X(03)00660-6
[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. doi: 10.1002/nme.1620372305
[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. doi: 10.1177/0021998307082178
[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. doi: 10.1016/S0141-0296(03)00078-6
[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. doi: 10.1016/S0045-7949(02)00249-3
[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. doi: 10.1016/j.jsv.2003.11.013
[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. doi: 10.1016/j.compstruc.2003.08.001
[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. doi: 10.1016/j.jsv.2006.09.003