Discontinuous Grazing Bifurcations-Induced Subharmonic Responses of a 2DOF Freeplay Airfoil System

Freeplay nonlinearities exhibited in aeroelastic systems can result in catastrophic aeroelastic instabilities such as limit cycle oscillations, chaos and abrupt bifurcations. Developing more advanced and accurate analytical models for the freeplay problem has attracted growing interest in the field of nonlinear aeroelasticity in recent years. Unfortunately, studies on higher-dimensional systems with freeplay rely mostly on numerical methods, which can provide responses under specific parameter conditions but make it difficult to evaluate the underlying mechanisms of the system’s dynamical behavior. Indeed, the system’s complex dynamic behavior is characterized by grazing bifurcations at the switching manifold, as well as its subharmonic responses. This paper develops a semi-analytical method based on switching manifolds and the mappings they generate. A two-degree-of-freedom airfoil model with freeplay nonlinearity is constructed and used as an example to analyze the subharmonic responses induced by grazing bifurcations. The results indicate that there are two mechanisms leading to grazing bifurcation in the system: continuous and discontinuous. Furthermore, the relationship between the system’s subharmonic responses and grazing bifurcations is comprehensively discussed. The proposed method contributes to a better understanding of freeplay systems.