Tailoring Damping and Nonlinearities in Self-Excited Mechanical Systems

在大多数机械工程系统中，振动是不需要的。自激振动尤其如此，表现为汽车和火车的刹车尖叫声、直升机的地面共振、架空传输线的飞跃振动、油膜轴承中高速转子的不稳定等等。在其中一些系统中，自激振动的后果可能是灾难性的。因为到目前为止，还没有一个系统存在普遍接受的解决方案。所有这些振动现象都有一个共同点，那就是它们的线性化运动方程中都存在循环项。在上面提到的每个例子中，它们都有不同的物理起源。最近，人们通过避免频谱中的对称性来优化机械结构对自激振动的稳健性，得到了新的结果。最近，人们系统地研究了循环项与不同形式的阻尼项的相互作用，并发现了一些令人惊讶的新结果。众所周知，阻尼可能会导致循环系统的不稳定和自激振动，但大多数知识都是针对极少数自由度的系统建立的，而不是以系统的方式建立的。在工程结构的运动方程中，循环项很难改变，但阻尼通常是可以修改的，尽管通常只能通过某些方式改变阻尼矩阵。在本项目中，将系统地研究表征线性机械系统的不同矩阵(惯性、刚度、陀螺、阻尼和循环)之间的相互作用，以期设计出对自激振动具有更强稳健性的结构。该项目首先将重点放在自治的线性系统上，后来还将扩展到时间周期和非线性系统。预计这将导致改进上述系统的设计方法，以期增加对自激振动的稳健性，或至少通过减少极限环来减轻其后果。

In most mechanical engineering systems vibrations are unwanted. This is particularly true for self-excited vibrations, which manifest themselves as brake squeal in cars and trains, ground resonance in helicopters, galloping vibrations of overhead transmission lines, instabilities of high-speed rotors in oil-film bearings, among others. In some of these systems the consequences of the self-excited vibrations can be catastrophic. For none of the systems universally accepted solutions exist so far. All these vibration phenomena have in common that circulatory terms are present in their linearized equations of motion. They have different physical origins in each of the examples mentioned above. In the recent past, new results were obtained for optimizing the robustness of mechanical structures with respect to self-excited vibrations by avoiding symmetries in the spectrum. Even more recently, the interaction of circulatory terms and different forms of damping were studied systematically and some surprising new results were found. It was of course well known that damping may cause instability and self-excited vibrations in circulatory systems, but most of this knowledge was established for systems with a very small number of degrees of freedom only and not in a systematic way.In the equations of motion of engineering structures, the circulatory terms are difficult to alter, but damping usually can be modified, although in general the damping matrix can only be changed in certain ways. In the present project, the interaction of the different matrices characterizing a linear mechanical system (inertia, stiffness, gyroscopic, damping and circulatory) will be studied systematically, with view to designing structures with a greater robustness with regard to self-excited vibrations. The project will first be focused on autonomous linear systems and later also expanded to time-periodic and nonlinear systems. It is expected that this will lead to improved design methods for systems such as the ones mentioned above, with view to increasing the robustness against self-excited vibrations or at least to mitigate their consequences by reducing the limit cycles.