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，它表现为汽车和火车刹车时的尖叫、直升机的地面共振、架空输电线路的飞驰振动、油膜轴承高速转子的不稳定等。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，还没有一个被普遍接受的解决方案存在。所有这些振动现象都有一个共同之处，即在它们的线性化运动方程中存在循环项。在上面提到的每个例子中，它们都有不同的物理起源。在最近的过去，通过避免谱中的对称性来优化机械结构相对于自激振动的鲁棒性获得了新的结果。最近，对循环项和不同形式阻尼的相互作用进行了系统的研究，并发现了一些令人惊讶的新结果。当然，众所周知，阻尼可能会导致循环系统的不稳定和自激振动，但大多数这方面的知识都是针对自由度非常小的系统建立的，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，但阻尼通常可以改变，尽管阻尼矩阵一般只能通过某些方式改变。在本项目中，将系统地研究表征线性机械系统（惯性，刚度，陀螺仪，阻尼和循环）的不同矩阵的相互作用，以期设计具有更大鲁棒性的自激振动结构。该项目将首先集中在自主线性系统，后来也扩展到时间周期和非线性系统。预计这将导致诸如上述系统的改进设计方法，以增加对自激振动的鲁棒性，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.