PEER has just published Report No. 2014/02 titled “Theoretical Development of Hybrid Simulation Applied to Plate Structures” as a new addition to the PEER Report Series. It was authored by Ahmed A. Bakhaty, Khalid M. Mosalam, and Sanjay Govindjee
Hybrid simulation is a popular testing method for the experimental assessment of structural systems. The primary notion is to test only part of the system physically while simultaneously simulating the rest of the system via computer. While the basic idea is simple to understand, there is surprisingly little theoretical work targeted towards understanding the behavior of the concept and in particular its theoretical limitations. Although much attention has been devoted to reducing perceived error, little is actually known about what the reduction targets should be. In this report an initial investigation of the theoretical limitations of hybrid testing is presented in the context of a simple canonical setting: the Kirchhoff-Love plate bending dynamic problem. The physical system is mathematically separated into two pieces whose motions are exactly integrated analytically in closed-form. At the splitting interface, theoretical models associated with tracking and phase error of the boundary motions and forces are introduced. A parametric study is then performed to assess the resulting dependency of the error in the system response in terms of the interface models. Errors are represented in terms of a variety of norms, including L2 norms, as well as a collection of semi-norms representing a variety of physically relevant resultant force-like quantities.
It is demonstrated that such systems are generally viable only below the first fundamental frequency of the system. At and above the fundamental frequency of the system, there are significant and unpredictable errors. Furthermore, it is shown that there is a tendency to accumulate global errors at the slightest introduction of any interface matching error, but that these errors become insensitive to further increase in mismatch. Finally, it is found that the different substructures are subject to excitation at their independent natural frequencies in addition to the natural frequencies of the hybrid system. Thus, in general, one needs to check both the natural frequencies of the whole as well as sub-systems in system design.