On the computation of compatible trajectories for hydraulic shaketables

Dynamic testing is often used to study the response of structures under earthquake loading. Such testing is either carried out with a prescribed input such as an earthquake ground motion, or using computation-in-the-loop, where a physical substructure is made to interact with a virtual substructure. This latter form of dynamic testing is also referred to as hybrid simulation. In both cases, the test system consisting of the physical test-piece, the actuators and sensors, controls, and other computations, constitutes a dynamic system that is different from the structure whose behavior is the focus of the test. It is therefore of interest to ask if there are trajectories of the test system that are compatible with desired trajectories of the structure tested. In this paper, we formulate this problem of finding compatible trajectories, as a nonlinear least-squares problem, and propose optimization strategies. We discuss the trajectory computation with two examples, seismic testing with prescribed ground motion, and hybrid simulation with a shaketable as the transfer system.