Assessing the effect of nonlinearities on the performance of a tuned inerter damper

In this paper, the use of a tuned inerter damper (TID) as a vibration absorber is studied numerically and experimentally, with civil engineering applications in mind. Inerters complete the analogy between mechanical and electrical networks, as the mechanical element equivalent to a capacitor and were developed in the 2000s. Initially, inerters were used for applications in automotive engineering, where they are known as J-dampers. Recently, research has suggested that inerter-based networks could be used for civil engineering applications, offering interesting advantages over traditional tuned mass dampers. In the civil engineering context, research has been mainly theoretical, considering ideal inerters. Because the dynamics of an inerter device include nonlinearities, especially at the low frequencies associated with civil engineering applications, the performance of the TID device using an off-theshelf inerter has been experimentally tested in the work presented here. The chosen system, comprising a host structure with a TID attached to it, was tested using real-time dynamic substructuring (RTDS) or hybrid testing. The inerter was tested physically, while the remaining components of the TID device, the spring and damper, together with the host structure, were simulated numerically. Displacements and forces at the interface between numerical and physical components are updated in real time. This numerical-physical split allows the optimisation of the TID parameters, because the values of the spring and the damper can be changed without altering the experimental setup. In addition, this configuration takes into account the inerter's potentially complex dynamics by testing it experimentally, together with the characteristics of the host structure. Developing RTDS tests for physical inertial substructures, where part of the fed back interface forces are proportional to acceleration, is a challenging task because of delays arising at the interface between the experimental and the numerical substructures. Problems associated with stability issues caused by delay and causality arise, because we are dealing with neutral and advanced delayed differential equations. A new approach for the substructuring algorithm is proposed, consisting of feeding back the measured force deviation from the ideal inerter instead of the actual force at the interface. The experimental results show that with appropriate retuning of the components in the TID device, the performance in the TID incorporating the real inerter device is close to the ideal inerter device. (C) 2016 The Authors. Structural Control and Health Monitoring published by John Wiley & Sons, Ltd.