AI 中文总结
本文建立一般两自由度系统的临界阻尼概念，发现其阻尼矩阵非对角且固有频率差异大时非正定，需主动元件实现，为该领域研究揭示了意外现象与陷阱。
AI 中文摘要
在这篇简报中，我们为一般两自由度系统建立了临界阻尼的概念。对于给定的一组质量和刚度，临界阻尼对应着重数最大的实特征值，其值等于固有频率的几何平均值的相反数。该情况对应一般初始条件下最快的渐近衰减率。临界情况的阻尼矩阵在一个模态坐标反射下是唯一的，且通常是非对角的。令人惊讶的是，当固有频率差异较大时，该阻尼矩阵也不是正定的。因此，临界情况的物理实现将需要提供负有效阻尼的主动元件。
英文摘要
In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping corresponds to the real eigenvalue with maximal multiplicity, equal to minus geometrical mean of the eigenfrequencies. This case corresponds to the fastest possible asymptotic decay rate for generic initial conditions. The damping matrix for the critical case is unique up to reflection of one modal coordinate and, generically, non-diagonal. Quite surprisingly, for large difference of the eigenfrequencies, it is also not positive definite. Therefore, physical realization of the critical case will require active elements that provide negative effective damping.
Comments7 pages, 2 figures
