Frictional damping effects on structural dynamics

该博士项目是由EPSRC和Rolls-Royce plc赞助的工业案例（IC）。它属于EPSRC研究领域“机械结构和系统的性能和检查”。该项目的重点是发展对振动结构的摩擦阻尼效应的基本理解。在节理结构中，在不同部件之间的界面上产生的摩擦会导致有害的影响，如噪音、磨损和疲劳损伤。然而，摩擦阻尼也可以起到能量耗散、隔离和振动控制等目的。摩擦阻尼器通常用于一些工程系统，包括民用建筑和涡轮机械。然而，由于摩擦阻尼的一些行为，如接触部件的周期性或永久性粘滞，或在特定频率范围内动态响应的放大，如果在设计阶段未考虑，可能会导致效率损失和意外故障。因此，更深入地了解这些现象，以及开发可靠的方法来监测工程结构中的摩擦，不仅对于防止故障，而且对于探索创新和有效的设计解决方案（包括摩擦阻尼器）至关重要。目前对摩擦阻尼效应的理解仍然有限，即使在简化结构模型、动载荷和摩擦力的假设时也是如此。因此，本项目遵循的研究策略包括开发一系列案例研究，其中离散单自由度（SDOF）和多自由度（MDOF）质量弹簧系统受到谐波载荷和库仑摩擦的影响。这些力学模型通常是在建筑物、叶片盘、机械悬架、制动系统等结构的早期设计阶段考虑的，并允许对其全局动态行为进行高层调查。在离散力学模型中，通常通过考虑系统的一个质量与地面固定墙之间的接触来引入摩擦阻尼。然而，在工程应用中，如燃气轮机叶片的燕尾接头或位于建筑物两层之间的摩擦阻尼器，两个振荡部件之间发生摩擦接触。在上述案例研究中，这个问题也通过考虑系统的两个不同质量之间或质量与振荡基座之间发生的摩擦接触来解决。采用理论、数值和实验相结合的方法研究了这些摩擦阻尼系统的动力特性。本研究解决的主要挑战是：-根据问题的物理参数，确定摩擦接触中的相对运动何时以连续，粘滑或粘滞运动为特征；-了解摩擦阻尼如何影响动态响应的特征，如共振、不变点、低频和高频行为；-开发从结构响应特征中检测和量化摩擦的实验技术和指标。前两个挑战是通过推导解析封闭解和开发有效的数值方法来解决的。迄今为止，该研究已经深入了解了摩擦阻尼对响应特征（如共振、不变点、低频和高频行为）的影响。此外，分析解决方案导致了二维地图的发展，允许在设计阶段快速预测运动状态。最后，对单层和二层剪力框架进行了实验研究，为理论结果提供了验证，并进一步深入了解了金属对金属接触的行为。

This DPhil project is an Industrial Case (IC) sponsored by EPSRC and Rolls-Royce plc. It falls within the EPSRC research area "Performance and inspection of mechanical structures and systems". The project focuses on the development of a fundamental understanding of friction damping effects on vibrating structures. In jointed structures, the friction generated in the interfaces between different components is known to lead to detrimental effects, such as noise, wear and fatigue damage. However, friction damping can also serve purposes such as energy dissipation, isolation and vibration control. Friction dampers are commonly used in several engineering systems, including civil buildings and turbomachines. Nonetheless, some behaviours due to friction damping, such as the periodic or permanent sticking of the parts in contact or the amplification of the dynamic response within certain frequency ranges, can lead to losses of efficiency and unexpected failures, if unaccounted during the design stage. Therefore, a deeper understanding of these phenomena, as well as the development of reliable approaches for monitoring friction in engineering structures, are essential not only to prevent failures but also to allow the exploration of innovative and efficient design solutions including friction dampers.The current understanding of friction damping effects is still limited, even when simplifying assumptions are considered for structural models, dynamic loadings and friction forces. Therefore, the research strategy followed in this project consists in the development of a series of case-studies where discrete single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) mass-spring systems are subjected to harmonic loadings and Coulomb friction. These mechanical models are typically considered during the early design stages for structures such as buildings, bladed-disks, mechanical suspensions, braking systems and many others, and allow a high-level investigation of their global dynamic behaviour. In discrete mechanical models, friction damping is usually introduced by considering a contact between one of the masses of the system and a ground-fixed wall. Nonetheless, in engineering applications such as the dovetail joints in gas-turbine blades or the friction dampers located between two different storeys of a building, friction contacts occur between two oscillating components. In the above case-studies, this problem is addressed by also considering friction contacts occurring between two different masses of the system or between a mass and an oscillating base.The dynamic behaviour of these friction damped systems is investigated by combining theory, numerical and experimental approaches. The main challenges addressed from this investigation are:- establishing when the relative motion in a friction contact is characterised by a continuous, stick-slip or stuck motion regime depending on the physical parameters of the problem; - understanding how friction damping affects features of the dynamic response such as resonances, invariant points, low- and high-frequency behaviours; - developing experimental techniques and metrics for detecting and quantifying friction from the response signature of a structure. The first two challenges are addressed by deriving analytical closed-form solutions and developing effective numerical approaches. To date, this study has provided an in-depth understanding of friction damping effects on response features such resonances, invariant points, low- and high-frequency behaviours. Moreover, analytical solutions led to the development of 2-D maps allowing a quick prediction of the motion regime during the design stage. Finally, experimental investigations have been carried out on single- and two-storeys shear frames, providing a validation for the theoretical results and a further insight on the behaviour of metal-to-metal contacts.