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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Stability of weakly damped MDGKN-systems: The role of velocity proportional terms
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Stability of weakly damped MDGKN-systems: The role of velocity proportional terms

机译：弱阻尼MDGKN系统的稳定性：速度成比例条款的作用

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摘要

Many problems in mechanical engineering, in the linearized case, can be modeled as a second order system of differential equations of type MDGKN, where the matrices correspond to inertia, damping, gyroscopic, stiffness, and circulatory forces. The latter may lead to self-excited vibrations which in general are unwanted and sometimes dangerous. It is well known that circulatory systems (N ≠ 0) are very sensitive to damping and their stability behavior may strongly depend on the structure of the damping matrix [4,5,7]. Moreover, it has been known for a long time, that the addition of (even infinitesimally small) damping may also destabilize such systems [1,17]. The present note studies in more detail some of the effects of velocity proportional terms on the stability of mechanical systems of this type. The aim is to extend the findings recently presented by HAGEDORN et al. in [4]. Therefore, the analytically derived stability boundary of an MDGKN-system with two degrees of freedom is analyzed with regard to infinitesimally small, incomplete, and indefinite damping matrices as well as the role of gyroscopic terms and the spacing of the eigenfrequencies.
机译：机械工程中的许多问题在线化的情况下，可以被建模为MDGKN类型的差分方程的二阶系统，其中矩阵对应于惯性，阻尼，陀螺，刚度和循环力。后者可能导致自我激发的振动，通常是不受欢迎的，有时是危险的。众所周知，循环系统（N≠0）对阻尼非常敏感，并且它们的稳定性行为可能强烈地取决于阻尼基质的结构[4,5,7]。此外，已经知道了很长时间，所以添加（甚至无限小）阻尼也可能破坏这种系统[1,17]。本发明的注意事项更详细地研究了速度比例术语对这种类型的机械系统稳定性的影响。目的是扩展最近由Hagedorn等人呈现的调查结果。在[4]中。因此，关于无限的小，不完全和无限的阻尼矩阵以及陀螺术语的作用和特征犯罪的间距，分析了具有两度自由度的MDGKN系统的分析衍生稳定性边界。

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