SUMMARY
The time‐integration algorithm is an indispensable element to determine response of the boundary of the numerical as well as physical parts in a hybrid test. Instability of the time‐integration algorithm may directly lead to failure of the test, so stability of an integration algorithm is particularly important for hybrid testing. The explicit algorithms are very popular in hybrid testing, because iteration is not needed. Many unconditionally stable explicit‐algorithms have been proposed for hybrid testing. However, the stability analysis approaches used in all these methods are valid only for linear systems. In this paper, a uniform formulation for energy‐consistent time integrations, which are unconditionally stable, is proposed for nonlinear systems. The solvability and accuracy are analyzed for typical energy‐consistent algorithms. Some numerical examples and the results of a hybrid test are provided to validate the effectiveness of energy‐consistent algorithms.
The applicability of the proposed dynamic response model for buildings is investigated using shaking‐table tests with a four‐storey steel specimen. This approach derives the equation of motion for a multi‐degree‐of‐freedom linear building based on microtremor measurements. Under a linear assumption, the equation can estimate the seismic response accelerations, velocities, and displacements at microtremor sensor locations without the need for information about the mass, damping, stiffness matrices or need for structural design documents to estimate peak responses that are linked with seismic damages of structural and non‐structural components. The modelling is unconstrained by structural shape, composition of frames, connections of structural members, or the assumption of a rigid floor. In comparison to the previous methods assuming simple/regular building shape with standard/typical rigid floor, the proposed model is applicable to large‐scale low‐rise buildings with irregular shapes, flat expanses, and open spaces such as large atria and skylights as well. The applicability study considers two practical scenarios: natural frequencies and damping ratios based on microtremors that can be updated by an earthquake and a standard assumption for structural design. The prediction accuracy is best when the participation vector for seismic input is obtained from sensors located on the upper floors; the structure mostly exhibits elastic response; a modal system identification is applied to the seismic measurement; and local damage does not affect the global seismic response of the structure. The reason is that this method assumes that identified mode shapes do not change due to the occurrence of an earthquake.
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