Numerical Stability Analysis Of Substructure Testing

Substructure testing is a hybrid method consisting of physical load and numerical simulations, in which the critical part of the overall structure, referred to as experimental substructure (ES), is tested with experimental facilities in laboratory while the remainder, called numerical substructure (NS), is simulated with numerical models in a computer. Substructure testing is prior to shaking table tests and pseudo dynamic testing due to possible larger test scale and more effective experimental cost. In addition, the real-time substructure testing (RST) method lately developed has combined the advantages of conventional dynamic testing techniques. Therefore, compared with other structural testing techniques, the substructure testing technique could better meet the requirement of the modern development of structural engineering. Moreover, the modern industrial technology and network can enhance performance of substructure testing.Nowadays, the substructure testing method is applied only to the structural components or small structures. Researchers have focused on the promotion of the stability and reliability of the substructure testing for wide applications to the complicated structures, and some meaningful results were obtained. This thesis concentrates on the stability of the substructure testing and the main contents are summarized as follows:Firstly, the stability of the central difference method for RST is investigated on a single degree-of-freedom structure. In this study, the experimental substructure is a spring-mass oscillator with a damper. It is demonstrated that the stability decays with the increasing mass ratio of the ES to the NS. When the mass ratio is not less than one, the integration algorithm is unconditionally unstable, while the algorithm is conditionally stable when this parameter is less than one. It is also found that the stability limit for this specimen is smaller than that for a pure mass specimen with the same mass ratio, and that the stability limit decreases with the increasing damping ratio of the ES. In addition, the stability limit is not influenced by the frequency ratio of the ES to the NS and the damping ratio of the NS. Meanwhile, zero-stability analysis is also carried out for the pure mass specimen. The theoretical results for the pure mass specimen were verified by experimental studies.Secondly, the stability analysis of the central difference method is conducted for RST on a two degree-of-freedom structure split into two substructures without any shared degree-of-freedom. Three methods have been considered, i. e. the movement quantities based method, series force based method and paralleling force based method. It is shown in this study that the stability limit decreases with the increasing of the mass ratio of the second floor to the first floor and the frequency ratio of the second floor to first floor with these three methods. The stability limit will increases with the damping ratio of the higher floor. When the damping ratio is zero, all of these three methods are unconventionally unstable. When the mass ratio and the frequency ratio are both relatively small or the damping ratio of the first floor is relatively large, stability limit of the force based control method is larger than that of the response based control method. Especially, stability threshold of the series force based control method is larger than that of the conventional central difference method which stability limit is equal to 2.Thirdly, the stability study of the average acceleration method, implicit mid-point method is performed with nonlinear stability approaches in this thesis. It is shown that for the dissipative nonlinear structure, the implicit mid point method is unconditionally stable but the average acceleration method may be conditional stable. This thesis proposes an equivalent control force control algorithm with implicit mid point integration method. This method is also verified by a pseudo dynamic test of a full scale three-story concrete structure. The four target displacements are calculated paralleling and four actuators are operated independently with Flex Test GT of MTS. Comparisons between the central difference method with the implicit mid point method of the test show that the stability of the implicit mid point method is more better.Lastly, the effect of time delay to the stability of integration algorithms for substructure testing is investigated. It is shown that the stability is improved by using implicit mid point method while that is worsen by using the central difference method. Therefore, on the one hand, it is necessary to conduct the stability analysis of the influence of time delay combining integration algorithms. On the other hand, the satisfactory stability performance of implicit mid point is proven in this thesis. The calculation expression is proposed of the time interval between the achieved displacement time histories and the desired displacement time histories. The approximation expression of the critical stability limit is proposed. It is illustrated that the small time step may not contribute to the stability of the testing and too many interpolation points may result in the instability of testing when the time scale and time delay of the step response are constant value of the actuator.