Robust stabilization and anti-resonance in parametric circulatory systems

参数循环系统中的鲁棒稳定和抗共振

• 批准号: 431399977
• 负责人: Professor Dr. Peter Hagedorn
• 金额: --
• 依托单位: Arbeitsgruppe Dynamik und Schwingungen
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/431399977?language=en
• 关键词: Robust; stabilization; anti; resonance; parametric

In this project we intend to study the stabilization of self-excited vibrations via parametric vibrations in circulatory systems. Dohnal coined the term parametric anti-resonance for stabilization of selfexcited vibrations through parametric excitation, although first examples were also found earlier by Tondl. Dohnal considered only systems with self-excitation due to nega¬tive damping and in phase parametric excitation in the stiffness matrix. In many cases of selfexcited systems, the self-excitation is however due to circulatory terms, rather than ‘negative damping’. Dohnal also explicitly excluded internal resonances and near resonances. These can however be quite important, since double eigenfrequencies are common in symmetric systems, and near internal resonances correspond to imperfectly balanced rotors, or other perturbations of symmetry, which are very common in engineering systems. Finally, the nonsynchronous parametric excitation, present in mechanical engineering systems with sliding contacts between parts, gives rise to very complex dynamical behavior (e.g. ‘total instability’ in the Cesari equations) and this has not been fully studied for circulatory systems. The cause of parametric resonance and anti-resonance was postulated by Dohnal to lie in an energy transfer between vibration modes, but never explored thoroughtly. This research should lead to a better understanding of so far not completely understood phenomena in self-excited systems (e.g. Why do brakes squeal at low speed only?) and can be of importance to many systems in engineering and possibly also in physics (see e.g. the particle trap, for which Wolfgang Paul received the Nobel Prize in 1989). Nonlinear parametrically excited systems will also be studied in this context, including the different bifurcations and limit cycles.

在这个项目中，我们打算通过电路系统中的参数振动来研究自激发振动的稳定。 Dohnal通过参数兴奋创造了一种术语参数抗谐振，以稳定自激发振动，尽管TONDL早些时候也发现了第一个示例。 Dohnal仅考虑了由于消极的舞蹈和刚度矩阵中的相位参数兴奋而引起的自激振动的系统。但是，在许多自我激发系统的情况下，自我激发是由于电路术语而不是“负舞”。 Dohnal还明确排除了内部共振和接近共振。但是，由于双重特征频率在对称系统中很常见，因此它们可能非常重要，并且近乎内部共振对应于不完美平衡的转子，或者其他对称性的扰动，这在工程系统中很常见。最后，在零件之间具有滑动触点的机械工程系统中存在的非同步参数激发产生了非常复杂的动态行为（例如，切萨里方程中的“总不稳定性”），并且尚未对电路系统进行全面研究。 Dohnal发布了参数共振和反谐振的原因，以置于振动模式之间的能量转移，但从未诚实地探索。这项研究应该导致对迄今为止的自我激发系统中的现象的更好理解（例如，为什么仅在低速下尖叫？），对于工程中的许多系统而言，也可能很重要，并且在物理学上也可能很重要（例如，参见Wolfgang Paul在1989年获得诺贝尔奖的粒子陷阱）。在这种情况下，非线性参数激发系统也将进行研究，包括不同的分叉和限制周期。