Basic examination of two substructuring schemes for shake table tests

Abstract

This study examines two basic substructuring schemes for shake table tests where the dynamics of the table is significantly affected by a specimen. The hybrid simulation (HS) scheme, commonly adopted in substructuring experiments, directly uses the output of a numerical substructure as an input signal to a physical substructure. The dynamical substructuring system (DSS) scheme, developed long after HS, uses feedforward and feedback controllers to minimise the control error produced by the outputs of numerical and physical substructures. Before examining these two schemes, this study introduces a systematic formulation for dividing a multi-degree-of-freedom emulate system into a numerical substructure and a physical substructure with a shake table. Then, controller designs for HS and DSS are discussed for the substructures. The two schemes with basic control approaches were numerically examined through substructuring tests for a linear 3DOF emulate system. DSS with stability was powerful even under a control condition with a pure time delay and inaccurate estimation of the table dynamics, whereas these factors degraded the HS performance. In additional simulations in which nonlinear characteristics were considered, the performance of DSS (HS) was degraded mainly by the nonlinear (inaccurate estimation of the table dynamics). It was found that the stability of substructures with nonlinear characteristics could be roughly assessed by the Nyquist stability criterion. These simulations with/without nonlinear characteristics clarified the performances of the HS and DSS schemes through basic control approaches and stability analysis under practical conditions.