A model-order reduction framework for hybrid simulation based on component-mode synthesis

Testing of stiff physical substructures (PSs) still poses major technical issues that prevent from adopting hybrid simulation (HS) as a standard structural testing method. Firstly, elastic deformation of reaction frames, as well as the limited resolution of displacement transducers, deteriorate displacement control accuracy. Secondly, as a consequence of control errors, small perturbations of actuator displacements entail large restoring force oscillations that spuriously excite the higher eigenmodes of the hybrid model. For this reason, in the current practice, force-controlled hydraulic jacks handle vertical degrees of freedom, which are typically associated with stiff axially loaded members and excluded from the time integration loop. Vertical forces are either kept constant or adjusted during the experiment based on simplified redistribution rules. Besides deterioration of displacement control accuracy, stiff PSs naturally increase the frequency bandwidth of the hybrid model, whose higher eigenfrequencies (divided by the testing time scale) may fall outside the frequency bandwidth of the actuation system, thus destabilizing the HS. This is a collateral issue to which, in the authors' knowledge, no sufficient attention as been dedicated yet, and this paper tries to address it. From this standpoint, we propose component-mode synthesis as a rigorous approach for deriving reduced-order physical and numerical substructure mass and stiffness matrices that minimize the frequency bandwidth of the hybrid model. The proposed methodology allowed for performing HSs of a load-bearing unreinforced masonry structure including both horizontal and vertical degrees of freedom with a standard three-actuator setup used for cyclic testing.