Investigation of Multiple Branches in Nonlinear Oscillators Using Real-Time Hybrid Testing

Abstract

The phenomenon of multiple branches of nonlinear structures occurs due to complex nonlinear interactions. They are difficult to detect and mainly investigated by numerical simulation. Commonly, path-following strategies are applied to gradually lead the nonlinear system into the desired branch. Once steady-state conditions have been determined, phenomena like isolated branches can be reproduced in dynamic simulations. However, neither the path-following strategy nor the specification of arbitrary initial conditions is generally possible in experimental dynamic testing. Nevertheless, if the effect of a nonlinear absorber on a nonlinear host structure is studied, the concept of real-time hybrid testing allows separating absorber and host structure. In this work, the absorber is tested experimentally, whereas the host structure is simulated in real time. Assuming proper coupling, the absorber can be tested under very realistic conditions, and stable states on arbitrary branches can be obtained following a two-step approach. First, the experimental subsystem is driven very close to the expected steady-state oscillation, then the real-type hybrid testing loop is closed by coupling the absorber with the simulation model, again with proper initial conditions. If the configuration of the overall system is adjacent to a desired stable branch, the system will converge to the branch within several oscillations. Once a desired configuration is reached, neighboring points can be studied by adapting the excitation frequency or amplitude. So far, the real-time hybrid testing results agree well with theoretical predictions and confirm that stable branches of nonlinear dynamic systems can be investigated using the proposed method.