Abstract This paper presents algorithms to compute eigenvalues, eigenvectors and frequency response matrix of a linear structure with non-proportional damping. The method is based on derivatives of repeated or unrepeated complex eigenvalues and complex eigenvectors . Since eigenvectors are not unique for a repeated eigenvalue, a special algorithm is developed to select the correct eigenvector for a given non-proportional damping. The advantage of the proposed method is that it only requires the knowledge of natural frequencies and mode shapes of the undamped structure. The validity of this method is established by comparing numerical results from this algorithm to exact answers.

中文翻译：

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计算非比例阻尼结构的特征值、特征向量和频率响应

摘要 本文提出了计算具有非比例阻尼的线性结构的特征值、特征向量和频率响应矩阵的算法。该方法基于重复或非重复复数特征值和复数特征向量的导数。由于重复特征值的特征向量不是唯一的，因此开发了一种特殊算法来为给定的非比例阻尼选择正确的特征向量。所提出方法的优点是它只需要了解无阻尼结构的固有频率和振型。该方法的有效性是通过将该算法的数值结果与精确答案进行比较来确定的。