Forced synchronization in a nonlinear aeroelastic system under external forcings

The ubiquitous presence of nonlinearities and multi-modal interactions has resulted in casting nonlinear fluid–structure interaction problems from the vantage of synchronization. A pivotal feature in these synchronization-based aeroelastic studies is the assumption of parametric/longitudinal flows, in turn, capable of giving rise to self-excited genres of nonlinear instabilities, such as limit cycle oscillations. However, in-field scenarios are fraught with external disturbances, which, in turn, have immense potential to jeopardize the stability characteristics. In the wake of the same, this study investigates the forced synchronization phenomena induced by vertical sinusoidal gust loads with the goal of illustrating the mechanisms by which external aerodynamic excitations govern the coupled structural mode dynamics. We consider a mathematical model of the nonlinear aeroelastic system by assuming a two-degree-of-freedom airfoil with cubic nonlinearity. The axial/parametric components of the flow are modeled through a typical unsteady aerodynamical formulation. The vertical/external wind load is assumed to be a sinusoidal forcing to facilitate a simplified analysis. Through numerical simulations and phase-locking metrics, we map the transitions from asynchronous and quasi-periodic oscillations to a phase synchronization in the response dynamics. The emergence of Arnold tongue structures enables a precise definition of the synchronization thresholds and illustrates how forcing intensity and frequency changes—particularly with frequency detuning—govern energy transfer between pitch and plunge modes with the external forcing. The study highlights the critical role of the modal frequency ratio in synchronization behavior and thereby providing valuable insight for possible strategies aimed at control of flow-induced instabilities and energy extraction. These findings have implications for the design and control of aeroelastic systems operating in turbulent, gusty environments, wherein tailored gust excitation may be exploited to stabilize or harness aeroelastic responses.