Substructure Hybrid Simulation with Multiple-Support Excitation

Substructure hybrid simulation of engineering structures subjected to multiple-support excitation (MSE) is investigated. In time-history analysis of MSE problems, the equations of motion are generally posed in relative coordinates (designated EOM-rel), which only require the ground acceleration as an input. However, the suitability of EOM-rel for hybrid simulation with MSE is unclear. Because estimating the tangent stiffness of the experimental substructure during testing is challenging, constant stiffness is often adopted in widely used integration schemes for hybrid simulation (e.g., the operator-splitting method); the equivalent force is not updated during experimentation. In previous studies, the equations of motion in absolute coordinates (designated EOM-abs) have been employed for hybrid simulation considering MSE. With EOM-abs, nonlinearity in the stiffness matrix is naturally considered in the measured restoring force—no approximation is involved. One drawback to EOM-abs is that the displacement and velocity of the ground motion must be computed prior to the experiment. This paper carefully formulates the hybrid simulation problem for structures subjected to MSE and examines the tradeoffs in the two approaches. First, the EOM-rel approximation and the EOM-abs are formulated and compared for a nonlinear single degree of freedom structure with nonlinearities modeled by a Bouc-Wen model subjected to two ground inputs. Significant error is found in the EOM-rel approximation because of the constant stiffness matrices used. Both formulations are then evaluated in hybrid simulation of a four-span highway ramp bridge. This study demonstrates that the EOM-rel approximation can provide results with good accuracy if the nonlinear components of the experimental substructure do not significantly affect the global stiffness matrix. Otherwise, the EOM-abs is recommended for hybrid simulation with MSE.