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

Abstract

Complex interactions of nonlinear structures often lead to diverse and unexpected effects. Phenomena like isolated branches typically occur at moderate to high vibration amplitudes. Even in numerical simulations, they are difficult to detect, and commonly path following strategies are used to determine a bifurcation point on the isolated branch. The majority of numerical investigations assume steady state conditions, and modifications in the system or excitation parameters are carried out carefully. However, many common concepts for numerical simulations are not available in experimental dynamic testing. Even for single degree of freedom systems, laboratory experiments of nonlinear structures are rather demanding because clearly defined nonlinearities are difficult to provide and identify. In this work, a Duffing type absorber is constructed and the required nonlinear forces are provided by permanent magnets. It is coupled to a host structure, which is also modeled as single degree of freedom Duffing oscillator. However, the model of the host structure is purely virtual, and realistic testing of the absorbing effects is obtained by a real-time hybrid testing approach. Assuming proper coupling, the absorber can be tested under very realistic conditions, and the concepts known from numerical investigations can be adapted to the proposed experimental setup. It is important that the coupled systems remain in steady state and therefore adjustments in the excitation are made slowly. Once a desired configuration is reached, neighboring points can be studied by adapting either the excitation amplitude or the excitation frequency. However, the physical system must remain on stable branches; thus, only the stable part of an isolated region can be reached. The experimental results indicate a very high sensitivity with respect to changes in amplitude, forcing, and nonlinear parameters, and therefore clearly defined laboratory conditions are essential. 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.