Operator-splitting method for real-time substructure testing. - Wu, Bin (Earthquake engineering & structural dynamics.)
It has been shown that the operator-splitting method (OSM) provides explicit and unconditionally stable solutions for quasi-static pseudo-dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real-time substructure testing (RST) when the velocity-dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM-RST algorithm are investigated. It is shown that the OSM-RST is unconditionally stable so long as the non-linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM-RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non-classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM-RST is preserved when the experimental substructure generates velocity-dependent reaction forces, whereas the stability of real-time substructure tests based on the central difference method is worsened by the damping of the specimen.