Homotopy Solution of the Inverse Generalized Eigenvalue Problems in Structural Dynamics
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摘要: 将结构动力学反问题视为拟乘法逆特征值问题，利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题，这种方法由于沿同伦路径求解，对初值的选取没有本质的要求，算例说明了这种方法是可行的．Abstract: The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.
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Key words:
- structural dynamics /
- homotopy method /
- inverse problem
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[1] 李书，冯太华，范绪箕.动力模型修正中逆特征值问题的数值解法[J].计算结构动力学及其应用，1995，12(3)：276—280. [2] 李书，卓家寿，任青文.对称结构动力设计中的广义逆特征值问题[J].计算力学学报，1999，16(2)：138—142. [3] 李书，卓家寿，任青文.动力模型参数识别中的Bayes方法[J].应用数学和力学，2000,21(4):402—408. [4] Joseph K T.Inverse eigenvalue problom for structural design[J].AIAA J,1992,30(12):2891—2896. [5] 曾庆华，张令弥.一种设计参数型的有限元模型修正方法[J].航空学报，1992，13(1)：A29—A35. [6] Friedland S,Nocedal J,Overton M L.The formulation and analysis numerical methods for inverse eigenvalue problem[J].SIAM J Numer Anal,1987,24(3):634—667. doi: 10.1137/0724043 [7] Allgower E,Georg K.Simplicial and continuation methods for approximating fixed points and solutions to systems of equations[J].SIAM Review,1980,(22):28—85. [8] Chu M T.Solving addition inverse eigenvalue problems by homotopy method[J].IMA J Numer Anal,1990，(9):331—342. [9] 徐树方.求解特征值反问题的同伦方法[J].计算数学，1993，15(2)：200—206. [10] 戴华.矩阵特征值反问题的若干进展[J].南京航空航天大学学报，1995，27(3)：400—413. [11] 周树荃，戴华.代数特征值反问题[M].郑州：河南科学技术出版社，1991. [12] Aruch M.Optimal correction of mass and stiffness matrices using measured modes[J].AIAA J,1982,20(11):1623—1626. doi: 10.2514/3.7995 [13] Aily R L.Eigenvector derivatives with repeated eigenvalues[J].AIAA J,1989,27(4):486—491. doi: 10.2514/3.10137 -
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