Tailoring Damping and Nonlinearities in Self-Excited Mechanical Systems

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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.