Atypical parametric instability in linear and nonlinear systems
Atypical parametric instability in linear and nonlinear systems
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线性和非线性系统中的非典型参数不稳定性
DOI：
10.1016/j.proeng.2017.09.118
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Daniel Hochlenert
中科院分区：
文献类型：
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作者：
Peter Hagedorn;Artem Karev;Daniel Hochlenert
参数激励的机械系统的运动方程的线性部分由M、D、G、K、N矩阵表征，这些矩阵可以都是时间周期的（分别是质量、阻尼、陀螺、刚度和循环矩阵）。这些系统的稳定性可以通过Floquet理论来研究。参数失稳行为的一个典型性质是存在组合共振。很久以前就已经知道，参数共振的类型在很大程度上取决于激励是在K矩阵中还是在N矩阵中，或者同时在它们两者中，其他矩阵是恒定的。在一般情况下，参数激励的问题进行了研究的情况下，所有的激励项是在相位。如果不是这种情况，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。这种类型的微分方程的例子最早是在70年前由Lamberto Cesari给出的，但似乎从那时起就被遗忘了。最近观察到，一个啸叫盘式制动器的最小模型的线性化运动方程有这样的相位参数激励。在方程中引入了附加的非线性项，并利用规范形理论计算了相应的极限环。
The linear parts of the equations of motion of parametrically excited mechanical systems are characterized by the M, D, G, K, N matrices which may all be time-periodic (mass, damping, gyroscopic, stiffness and circulatory matrices, respectively). The stability of these systems can be studied via Floquet theory. A typical property of parametric instability behavior is the existence of combination resonances. It has been known for a long time that the type of parametric resonance depends very much on whether the excitation is in the in the K or in the N matrices, or simultaneously in both of them, the other matrices being constant. In general, problems of parametric excitation are studied for the case in which all the excitation terms are in phase. If this is not the case, 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. Examples of differential equations of this type were first given about 70 years ago by Lamberto Cesari, but seem largely to have fallen into oblivion since then. It was recently observed that the linearized equations of motion for a minimal model of a squealing disk brake have such out of phase parametric excitation. Additional nonlinearities are introduced in the equations and the corresponding limit cycles are calculated using normal form theory.
DOI：
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发表时间：
2011
期刊：
影响因子：
--
作者：
D. Hochlenert
通讯作者：
D. Hochlenert