Analysis and Preliminary Experimental Study on Central Difference Method for Real-time Substructure Testing

Central difference method (CDM) that is explicit for pseudo dynamic testing is also supposed to be explicit for real-time substructure testing (RST). However, to obtain correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the necessary modification of standard central difference method when applied to RST and analyzes the stability of the modified CDM for RST (CDM-RST). The analysis shows that the stability of the CDM-RST decreases with increasing damping ratio of the physical substructure. Then a preliminary experimental research is described. The test shows that the calculated result agrees well with the tested one when the damping ratio of the specimen (i.e., damper) is relatively low, but the discrepancy between the tested and calculated responses increases with the increasing damping ratio of the specimen.