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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