Self-excited vibrations in time-variant systems

时变系统中的自激振动

基本信息

批准号：
267028366
负责人：
Professor Dr. Peter Hagedorn
金额：
--
依托单位：
Department of Mechanical Engineering
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/267028366?language=en
关键词：
Self excited vibrations time variant

项目摘要

Time-variant and in particular periodic mechanical systems are common in Machine Dynamics. The theory of linear time periodic differential equations was developed about a hundred years ago by Floquet. In applied mechanics, parametrically excited vibrations are studied with Floquet theory, which together with the particular structure of the equations of motion in mechanical systems leads to special phenomena (e.g. combination resonances). In the past, particularly conservative and stable linear systems were studied at length, which may become unstable due to additional parametric excitation (parametric resonance). In Machine Dynamics, however, usually these effects are only relevant for systems which are extremely weakly damped, and they therefore are only rarely observed in reality. They also tend to occur only in very narrow frequency ranges of the parametric excitation. More recently, time periodic mechanical systems have also become important in the context of self-excited vibrations. In a number of engineering systems, self-excitation appears in the equations of motion in the form of circulatory terms (skew symmetric matrices in the coordinate proportional forces). In many of these cases, the frequency of the parametrical excitation is much lower than that of the self-excited vibrations, so that parametric resonances in the usual sense do not play a role. Even so, the periodic coefficients may be crucial for stability. An example of this type of self-excited vibrations is break squeal. Ignoring the periodic coefficients in the numerical analysis usually leads to an overestimation of the susceptibility of a structure to become unstable, although in some cases it may also be underestimated. In the planned project, the influence of small periodic perturbations of the linearized equations of motion of circulatory systems will be studied. Subcritical and supercritical Hopf bifurcations as well as the domains of attraction of the different stationary solutions will be examined for nonlinear systems. For large periodic systems (many thousand or many hundred thousand degrees of freedom) it is planned to develop methods for dealing with the problem in a FEM environment, with the aim to allow an efficient stability analysis in this environment.

时间变化，特别是周期性的机械系统在机器动力学中很常见。线性时间周期性方程式的理论是由Floquet开发的。在应用力学中，使用浮雕理论研究了参数激发的振动，这与机械系统中运动方程的特殊结构一起导致特殊现象（例如组合共振）。过去，尤其是保守和稳定的线性系统的长度研究，由于其他参数激发（参数共振）可能会变得不稳定。但是，在机器动力学中，通常这些效果仅与受到极度弱减弱的系统有关，因此它们在现实中很少被观察到。它们还倾向于仅以参数激发的非常狭窄的频率范围出现。最近，时间周期性的机械系统在自激发振动的背景下也变得很重要。在许多工程系统中，自我激素以循环术语的形式出现在运动方程中（坐标比例力的偏斜对称矩阵）。在许多情况下，参数激发的频率远低于自激发振动的频率，因此通常意义上的参数共振不会发挥作用。即使这样，周期性系数也可能对稳定性至关重要。这种自激发振动的一个例子是断裂。忽略数值分析中的周期系数通常会导致对结构变得不稳定的敏感性的高估，尽管在某些情况下也可能被低估了。在计划的项目中，将研究循环系统运动方程的小型周期性扰动的影响。对于非线性系统，将检查亚临界和超临界的HOPF分叉以及不同固定溶液的吸引力领域。对于大型的周期系统（数千到数十万个自由度），计划开发用于在FEM环境中处理问题的方法，目的是允许在此环境中进行有效的稳定性分析。