Frictional damping effects on structural dynamics

这个DPhil项目是由EPSRC和劳斯莱斯公司赞助的工业案例(IC)。它属于EPSRC的研究领域“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减振影响的基本了解。在连接结构中，不同部件之间产生的摩擦会导致噪声、磨损和疲劳损伤等不利影响。然而，摩擦阻尼器也可以用于消能、隔震和振动控制等目的。摩擦阻尼器通常用于几个工程系统，包括民用建筑和涡轮机械。然而，由于摩擦阻尼引起的一些行为，例如接触部分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，如果在设计阶段没有考虑在内，可能会导致效率损失和意外故障。因此，深入了解这些现象以及开发可靠的摩擦监测方法，不仅对于防止结构失效，而且对于探索包括摩擦阻尼器在内的创新和有效的设计解决方案都是至关重要的。即使考虑到结构模型、动态载荷和摩擦力的简化假设，目前对摩擦阻尼器效应的理解仍然有限。因此，本项目所遵循的研究策略包括开发一系列案例研究，其中离散的单自由度(SDOF)和多自由度(MDOF)质量-弹簧系统承受简谐载荷和库仑摩擦。这些机械模型通常在建筑物、叶片盘、机械悬挂、制动系统和许多其他结构的早期设计阶段被考虑，并允许对其全局动态行为进行高水平的调查。在离散力学模型中，摩擦阻尼通常是通过考虑系统质量之一与地面固定墙之间的接触来引入的。然而，在工程应用中，如燃气轮机叶片中的燕尾连接或位于建筑物两个不同楼层之间的摩擦阻尼器，两个振动部件之间会发生摩擦接触。在上述算例研究中，通过考虑系统的两个不同质量之间或质量与振动基座之间的摩擦接触来解决这一问题。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学行为。这项研究涉及的主要挑战是：-确定摩擦接触中的相对运动何时表现为连续、粘滑或粘滞运动状态，取决于问题的物理参数；-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；-开发从结构的响应特征检测和量化摩擦的实验技术和度量标准。前两个挑战是通过推导解析的闭式解和开发有效的数值方法来解决的。到目前为止，这项研究已经提供了对摩擦阻尼对响应特征的影响的深入了解，如共振、不变点、低频和高频行为。此外，解析解决方案导致了2-D地图的开发，从而能够在设计阶段快速预测运动状态。最后，对单层和两层剪力框架进行了试验研究，验证了理论结果，并对金属-金属接触的行为有了进一步的了解。

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.