Asynchronous parametric excitation, total instability and its occurrence in engineering structures
Asynchronous parametric excitation, total instability and its occurrence in engineering structures
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工程结构中的异步参量激励、总体失稳及其发生
DOI：
10.1016/j.jsv.2018.05.003
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发表时间：
2018
影响因子：
4.7
通讯作者：
Daniel Hochlenert
中科院分区：
文献类型：
--
作者：
Artem Karev;Peter Hagedorn;Daniel Hochlenert
在机械工程系统中，自激振动和参数激励振动通常是不需要的，有时甚至是危险的。有许多系统表现出这种振动，直到今天还不能完全避免，例如制动尖叫，架空输电线路的驰振，直升机的地面共振等。在一般情况下，参数激励的问题研究的情况下，所有的时间周期项是同步的。在这种情况下，稳定性行为很好理解。然而，如果时间周期项是异步的，则可能发生“非典型”行为：线性系统可能对参数激励的所有频率都不稳定，而不仅仅是在某些离散频率的邻域内（总不稳定性）。直到最近，人们还认为这种“非典型”行为不会出现在机械系统中。本文讨论了异步参数激励下线性和非线性系统的一些最新见解和结果。用规范形方法证明了一类广义非线性系统的完全不稳定性，并计算了其极限环。此外，一个最小的盘式制动器模型，具有这样的相位参数激励的机械示例。该示例从工程角度概述了所观察到的效应的重要性，因为类似的项也预期在具有通风通道的盘的盘式制动器的运动方程中，并且很可能也在其他物理系统中。
In mechanical engineering systems self-excited and parametrically excited vibrations are in general unwanted and sometimes dangerous. There are many systems exhibiting such vibrations which up to this day cannot be completely avoided, such as brake squeal, the galloping vibrations of overhead transmission lines, the ground resonance in helicopters and others. In general, problems of parametric excitation are studied for the case in which all the time-periodic terms are synchronous. In this case the stability behavior is well understood. However, if the time-periodic terms are asynchronous, an “atypical” behavior may occur: The linear system may then be unstable for all frequencies of the parametric excitation, and not only in the neighborhood of certain discrete frequencies (total instability). Until recently it was believed that such “atypical” behavior would not appear in mechanical systems. The present paper discusses some recent insights and results obtained for linear and nonlinear systems with asynchronous parametric excitation. The method of normal forms is used to prove total instability and to calculate limit cycles of a generalized nonlinear system. Further, a mechanical example of a minimal disk brake model featuring such out of phase parametric excitation is presented. The example outlines the importance of the observed effects from the engineering point of view, since similar terms are also expected in the equations of motion of disk brakes with disks with ventilation channels and most likely also in other physical systems.
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