Comparisons of three numerical integration algorithms in shake table-actuator hybrid testing under proportional errors

•Equations of STAH tests with three numerical integration algorithms are derived.•Four sources of errors are concluded, and the proportional error is considered.•Proportional errors have effects on the stability and accuracy of the STAH tests.•The Chang Method is the most stable among all the three algorithms.•The LAM is the most accurate among all the three algorithms.

Shake Table-Actuator Hybrid (STAH) testing is a recently developed dynamic test method. A STAH test is in a certain sense a dynamic time history analysis of a structure under seismic loading, except that some nonlinear elements are tested in the laboratory. Therefore the numerical integration algorithm is significant for the accuracy of the structural seismic response. In order to compare the effects of different numerical integration algorithms, the stabilities and accuracies of STAH tests with Central Difference Method, Linear Acceleration Method and Chang Method are studied. In this paper, the equations of STAH tests with three different numerical integration algorithms are derived and then the numerical simulation platforms based on these algorithms are developed using the software MATLAB. Errors in seismic tests are inevitable, and proportional errors are the worst of all. Therefore the effects of proportional errors on the stability and accuracy of STAH testing are investigated. The effects of the three different numerical integration algorithms are also discussed and compared theoretically and numerical simulation platforms are used to verify the theoretical results. It turns out that the stability of Chang Method is better while the accuracy of Linear Acceleration Method is better. Therefore, it is suggested that different numerical integration algorithms should be adopted according to different situations.