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.

在分析非对称阻尼线性离散动力系统时，大多数针对设计参数的灵敏度算法都采用归一化关系与系统属性矩阵加权的关系。本文提出了两种基于欧几里得范数作为归一化条件的新方法（代数方法和直接方法）。开发了这两种提议的方法来计算非对称阻尼系统的复杂模态参数的一阶和二阶灵敏度。在提出的方法中还讨论了二阶泰勒近似的精度。像其他代数方法一样，本文概述了数值稳定性的证明。与Nelson的直接方法（“本征矢量导数的简化计算”，AIAA杂志）不同，卷 14（No. 9，1976，pp。1201–1205），本文考虑了复矢量空间中解空间的复杂性，提出的直接算法的划分方案更加实用。通过一参数数值实验和两参数数值实验证明了其有效性和正确性。