A complex networks based approach to nonlinear aeroelasticity

Abstract

The present study investigates the effect of low intensity additive noise on a subcritical pitch-plunge aeroelastic system through the lens of complex networks. In the deterministic system, the 0→ fixed point loses its stability at the flutter point, via subcritical Hopf bifurcation. The unstable LCO becomes a high-amplitude stable LCO at the turning point, posing danger to structural integrity. The system displays bi-stability, and an analysis of the basin stability has revealed it to be highly susceptible to external perturbations. The external perturbations, modelled here as a direct random forcing in the form of a Gaussian white noise, could drastically change the deterministic dynamics. It brought in new dynamical states like noise induced intermittency and an advancement in the onset of LCO. Phenomenological and Dynamical bifurcations (for the stochastic system) were tracked and found to capture only the qualitative changes. To quantify the changes in the dynamics, response time-series were converted into complex networks, based on recurrences in the phase-space. Various network theory based measures such as edge density, clustering coefficient etc., were successful in capturing the dynamical transitions well quantitatively and to potentially serve as precursors for the aeroelastic system. Average path length, global efficiency measures signified the average separation of states and the robustness of the attractor, respectively. The networks also displayed the famous “small-world” property, indicating that transition between states occurs through very few intermediate states. The results have shown that a careful consideration of the stochastic perturbations is needed in the design and operations of such systems, and that complex networks based methods are successful in providing novel perspectives on the topology of the phase-space.