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Homotopy solution of the inverse generalized eigenvalue problems in structural dynamics. (English) Zbl 1145.74421

Summary: 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.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:

[1] LI Shu, FENG Tai-hua, FAN Xu-ji Numerical solution of inverse problem in dynamic model updating[J].Journal of Computational Structural Mechanics and Applications, 1995,12(3):276–280. (in Chinese)
[2] LI Shu, ZHUO Jia-sou, REN Qing-wen. Inverse generalized eigenvalue problem in dynamic design of symmetric structures[J].Chinese Journal of Computational Mechanics,1999,16(2):138–142. (in Chinese)
[3] LI Shu, ZHUO Jia-shou, REN Qing-wen. Parameter identification of dynamic models using a bayes approach[J].Applied Mathematics and Mechanics (English Edition), 2000,21(4):447–454. · Zbl 0982.74520 · doi:10.1007/BF02463767
[4] Joseph K T. Inverse eigenvalue problom for structural design[J].AIAA J,1992,30(12):2891–2896. · Zbl 0825.73453 · doi:10.2514/3.11634
[5] ZENG Qing-hua, ZHANG Ling-mi. The method of finite element model updating of design parameter[J]Acta Aeronautica ET Astronautica Sinica,1992,13(1):A29-A35. (in Chinese)
[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. · Zbl 0622.65030 · 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. · Zbl 0432.65027 · doi:10.1137/1022003
[8] Chu M T. Solving addition inverse eigenvalue problems by homotopy method[J].IMA J Numer Anal, 1990,(9):331–342. · Zbl 0703.65024 · doi:10.1093/imanum/10.3.331
[9] XU Shu-fang. Homotopy method for computation the inverse eigenvalue problems[J].Numerical Mathematics a Journal of Chinese University, 1993,15(2):200–206. (in Chinese)
[10] DAI Hua. Some development for inverse matrix eigenvalue problems[J].Journal of Nanjing University of Aeronauics and Astronautics, 1995,27(3):400–413. (in Chinese) · Zbl 0851.65022
[11] ZHOU Shu-quan, DAI Hua.The Algebraic Inverse Eigenvalue Problem[M]. Zhengzhou: Henan Science and Technology Press, 1991. (in Chinese)
[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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