Stability analysis of substructure shake table testing using two families of model-based integration algorithms

Abstract In implementing a substructure shake table testing (SSTT), the complete structure is divided into the experimental and the analytical substructures, which are driven by shake table and numerically simulated in a computer, respectively. A number of unconditionally stable and explicit integration algorithms referred to as model-based algorithms with highly computational efficiency have been developed to meet the requirement of real-time in conducting SSTT. This study aims to comprehensively investigate the stability of the SSTT system using two recently proposed model-based integration algorithms with controllable numerical energy dissipation, i.e., Kolay-Ricles-α (KR-α) algorithms and modified KR-α (MKR-α) algorithms. The SSTT system for the 2-degree-of-freedom (2-DOF) structures are firstly formulated. In order to take the contribution of the experimental substructure into consideration, the dynamic condensation is adopted to calculate the integration parameters for the analytical substructure. The discrete transfer function of the 2-DOF-SSTT system are derived. The influences of the mass ratio, the frequency ratio and the time step on the stability of the SSTT system are comprehensively investigated by using the discrete control theory. The results show that for larger values of the mass ratio, the frequency ratio and the time step have negative impact on the stability of the SSTT system. In addition, a subfamily of the MKR-α algorithms along with the dynamic condensation can always ensure the SSTT system stable.

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