Abstract
Most of the sensitivity algorithms with respect to the design parameters adopted the normalization relationship with system property matrices weighted when analyzing an asymmetrical damping linear discrete dynamic system. In this paper, two new methods (an algebraic method and a direct method) based on the Euclidean norm as the normalization conditions are proposed. Both proposed methods are developed to calculate the first- and second-order sensitivities of the complex modal parameters for an asymmetric damped system. The precisions of the Taylor approximations of the second degree are also discussed in the proposed methods. Like other algebraic methods, this paper outlines the proof of numerical stability. Different from Nelson’s direct method (“Simplified Calculation of Eigenvector Derivatives,” AIAA Journal, Vol. 14, No. 9, 1976, pp. 1201–1205), this paper considers complexity of the solution space in complex vector space, and the partitioning scheme of the proposed direct algorithm is more practical. The usefulness and correctness are demonstrated by a one-parameter numerical experiment and a two-parameter numerical experiment.
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