A Virtual Mechanical System control law for energy transfer towards a single actuation point in [formula omitted] DOF buildings

Abstract

Mitigating vibrations in engineering structures is of key interest, as they can lead to failure and/or discomfort. However, in some cases it is not feasible to actuate all the structure’s degrees of freedom, which makes vibration mitigation difficult. In this work, we investigate the addition of a single one-degree-of-freedom virtual mechanical system (VMS), as an active controller, to attract and mitigate the energy from an impulse load on the structure. To challenge the controller, an actuation point is chosen furthest away from the impact location. As it is implemented virtually, the coupling between the structure and VMS can be chosen freely. It is found that a skew-symmetric coupling generates a gyroscopic force that enables control over the structure’s mode shapes. Using this, the controller is tuned to achieve a beating phenomenon that attracts the vibration energy to the actuation location. A nonlinear damper, based on the slope of the envelope of the virtual velocity state, avoids reflection of energy to the structure and dissipates this unwanted energy. Furthermore, the virtual damper’s robustness to timing errors is investigated: damping too soon means an incomplete energy transfer to the VMS, damping too late leads to return of energy to the building. The tuning strategy of the VMS is applied to a 4 DOF and 60 DOF building benchmark. For comparison, a tuned mass damper (TMD) and a nonlinear energy sink (NES) are tuned as well. The VMS succeeds in decreasing the settling time significantly in both cases, while the performance of the passive TMD and NES is rather limited for this specific configuration.