Some recent results on MDGKN‐systems
Some recent results on MDGKN‐systems
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MDGKN 系统的一些最新结果
DOI：
10.1002/zamm.201300270
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Kapuria
中科院分区：
文献类型：
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作者：
P. Hagedorn;E. Heffel;P. Lancaster;P. Müller;S. Kapuria
有限维自治力学系统的线性化运动方程通常表示为二阶系统，并且是MDGKN型的，其中不同的n × n矩阵具有某些特征性质。这些矩阵的性质有后果的基本特征值问题。工程师们已经对这种系统有了很好的直观理解，特别是对于没有陀螺项（G矩阵）和循环项（N矩阵，这可能导致自激振动）的系统。许多重要的工程问题的线性化形式描述了这类方程。长期以来，人们都知道，这种系统中的阻尼（D矩阵）可以使系统稳定或不稳定，这取决于矩阵的结构。在这里，我们提出了一些新的结果（使用各种方法的证明）的阻尼项的影响，这是相当普遍的。从一些图表开始，它们是作者在最近几个月里共同开发的。
The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the MDGKN type, where the different n × n matrices have certain characteristic properties. These matrix properties have consequences for the underlying eigenvalue problem. Engineers have developed a good intuitive understanding of such systems, particularly for systems without gyroscopic terms (G‐matrix) and circulatory terms (N‐matrix, which may lead to self‐excited vibrations). A number of important engineering problems in the linearized form are described by this type of equations. It has been known for a long time, that damping (D‐matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. Here we present some new results (using a variety of methods of proof) on the influence of the damping terms, which are quite general. Starting from a number of conjectures, they were jointly developed by the authors during recent months.