Improved control algorithm for real-time substructure testing

Real-time substructure testing is a novel method of testing structures under dynamic loading. The complete structure is separated into two substructures, one of which is tested physically at large scale and in real time, so that time-dependent non-linear behaviour of the substructure is realistically represented. The second substructure represents the surrounding structure, which is modelled numerically. In the current formulation this numerical substructure is assumed to remain linear. The two substructures interact in real-time so that the response of the complete structure, incorporating the non-linear behaviour of the physical substructure, is accurately represented. This paper presents several improvements to the linear numerical modelling of substructures for use in explicit time-stepping routines for real-time substructure testing. An extrapolation of a first-order-hold discretization is used which increases the accuracy of the numerical model over more direct explicit methods. Additionally, an integral form of the equation of motion is used in order to reduce the effects of noise and to take into account variations of the input over a time-step. In order to take advantage of this integral form, interpolation of the model output is performed in order to smooth the output. The improvements are demonstrated using a series of substructure tests on a simple portal frame. While the testing approach is suitable for cases in which the physical substructure behaves non-linearly, the results presented here are for fully linear systems. This enables comparisons to be made with analytical solutions, as well as with the results of tests based on the central difference method. Copyright (C) 2001 John Wiley & Sons, Ltd.