Tuned-Inerter-Based-Dampers with linear hysteretic damping for earthquake protection of building structures

The inerter is a two-terminal device that generates a resisting force proportional to the relative acceleration between its two terminals. To date, three main types of inerters have been introduced in the literature based on inertial mass (inertance) generation mechanisms: fluid inerters, rack-and-pinion inerters, and ball-screw inerters. In such mechanisms, significant levels of inertance can be generated while keeping the actual mass to a minimum. This feature of inerters has attracted many researchers in the earthquake engineering community to explore their use for protecting building structures against earthquakes. For this purpose, inerters are often combined with a stiffness and a damping element in various confiigurations to form so-called tuned-inerter-based-dampers (TIBDs). There are three TIBDs mostly found in the literature: (1) tuned-viscous-mass-damper (TVMD); (2) tuned-inerter-damper (TID); (3) tuned-mass-damper-inerter (TMDI). One common layout of the three TIBDs is they have at least two elements connected in parallel. In the TVMD, the two elements are viscous damper and inerter, while in the TID and TMDI, the two elements are spring and viscous damper. For the first time, the possibilities for the devices to exhibit hysteresis through the two elements in parallel are explored in this thesis. In particular, two linear hysteretic damping concepts are discussed: (1) complex damping; and (2) complex stiffness. Furthermore, novel concepts of passive tuned inerter dampers with linear hysteretic damping, namely the tuned inerter hysteretic damper (TIhD) and the tuned mass hysteretic damper inerter (TMhDI) are introduced. Both concepts were developed based on the well established TID concept whereby the parallel connected viscous damping and spring elements are replaced by a complex stiffness model. The idea is to design a more realistic tuned inerter damper that captures the hysteretic behavior of the dampers. The aim is to develop a modified method to solve the equation of motion of structures with complex stiffness in the time domain. Finally, a shake table experiment was performed for a three-storey structure equipped with a TMhDI device on its base storey, subjected to both harmonic and earthquake base inputs. The TMhDI uses gel dampers as its hysteretic damping element. The inerter element was realised by a flywheel inerter which was designed by using a frictionless linear guide mechanism. For comparison, a shake table experiment was also performed for the same three-structure equipped with a TMDI device on its base storey level. The viscous damping element was realised using eddy current dampers. It is shown that the analytical model of both TMhDI and TMDI are in good agreement with the experimental results. Furthermore, these experiments also confirm the distinction between both devices, particularly in the structure's second and third modes of vibrations, where the structure equipped with the TMhDI has a larger response.