Frictional damping effects on structural dynamics

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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.