Exploiting impact-induced Intermodal Targeted Energy Transfer (IMTET) for passive mitigation of resonant vibrations of rotationally periodic structures

目前的主要工程实践是尽可能地避免非线性，并且主要依靠线性分析。这项拟议的研究与目前的传统观点截然相反，因为它利用故意的强非线性来实现被动跨尺度能量传递(在线性区域中没有对应的能量传递)，以便以被动、稳健和可预测的方式达到前所未有的减振性能。为了诱导如此强烈的能量传递，一个小冲击器被自由地放置在结构的空腔中，该结构的振动将被减轻。与冲击阻尼器完全不同的是，这里的目标是避免接触区域的局部耗散。这具有避免损伤的重要优点，由于不需要描述非弹性碰撞和塑性接触损伤的经验定律，因此可以更好地预测系统的行为。相反，被动减振是通过跨模式定向能量转移(IMTET)实现的，即从低频模式到高频模式的不可逆能量转移，具有双重好处：首先，总体振动幅度随着振动频率的增加而减小，其次，高频模式可以更有效、更快速地耗散振动能量。本提案中为减轻振动而提出的跨频率(尺度)IMTET的灵感来自于自然系统中常见的类似的不可逆能量级联(例如，湍流)。IMTET的概念是最近发展起来的，到目前为止只分析了具有良好分离固有频率的隔震结构的情况。在本项目中，首次针对旋转周期结构(由于接近对称而固有地具有紧密间隔的模式)的情况分析了IMTET。在工程中可以找到许多这样的结构的例子，包括带叶片的涡轮盘、带端绕组的发电机和带腿的冷却塔。重点放在共振振动上，将使用适当的分析、计算和实验方法来研究IMTET的缓解效果，更具体地说，碰撞能量散射。首次分析了扇区间和扇区内IMTET对无序/失谐、扇区间耦合强度、离心力和不同耗散机制(气动、材料和干摩擦)的敏感性。该项目将与A·F·瓦卡基斯教授作为墨卡托研究员密切合作进行。

It is the current predominant engineering practice to avoid nonlinearities whenever possible and to rely mostly on linear analysis. The proposed research stands in polar opposite to the current conventional view, as it exploits intentional strong nonlinearity to enable passive cross-scale energy transfers (having no counterpart in the linear regime) in order to reach unprecedented vibration mitigation performance in a passive, robust and predictable way. To induce such intense energy transfers, a small impactor is placed freely into a cavity of the structure whose vibrations are to be mitigated. In complete contrast to the impact damper, the goal here is to avoid local dissipation in the contact region. This has the important advantages that damage is avoided, and the system behavior can be much better predicted since empirical laws to describe the inelastic impacts and plastic contact damage are not needed. Instead, passive vibration mitigation is achieved by intermodal targeted energy transfer (IMTET), i.e., irreversible energy transfer from low-frequency modes to high frequency ones, with a dual benefit: First, the overall vibration amplitude decreases as the frequency of vibration increases, and, second, vibration energy is dissipated much more effectively and rapidly by the high frequency modes. IMTET across frequencies (scales), as proposed in the present proposal for the purpose of vibration mitigation, is inspired by analogous irreversible energy cascades that occur commonly in natural systems (e.g., turbulence). The concept of IMTET has been developed quite recently and analyzed so far only for the case of isolated structures with well-separated natural frequencies. In this project, IMTET is analyzed, for the first time, for the case of rotationally periodic structures (which inherently have closely-spaced modes due to near symmetry). Many examples of such structures can be found in engineering, including bladed turbine disks, generators with end windings, and cooling towers with legs. A focus is placed on resonant vibrations, for which the mitigation efficacy of IMTET and, more specifically, impact energy scattering is to be investigated using appropriate analytical, computational and experimental methods. The sensitivity of inter-sector and intra-sector IMTET to disorder/mistuning, strength of the inter-sector coupling, centrifugal loading and different dissipation mechanisms (aerodynamic vs. material vs. dry frictional) is to be analyzed for the first time. The project will be carried out in close collaboration with Prof. A. F. Vakakis as Mercator Fellow.