阻尼线性系统的模态近似

摘要：

考虑有限维阻尼二阶系统，得到了相应的二次特征值问题的谱包含定理。包含集是'准卡西尼椭圆'，这可能大大优于标准的盖什戈林圈。作为未扰动系统，我们取系统的模态阻尼部分;这包括已知的比例阻尼模型，但可能给出更精确的估计。然后应用这些包含体导出了一个给定阻尼系统的过阻尼性的一些易于计算的充分条件。

英文摘要：

We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the 'quasi Cassini ovals' which may greatly outperform standard Gershgorin circles. As the unperturbed system we take a modally damped part of the system; this includes the known proportionally damped models, but may give much sharper estimates. These inclusions are then applied to derive some easily calculable sufficient conditions for the overdampedness of a given damped system.

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