Flutter is a potentially destructive singularity that occurs when the aerodynamic forces generated by fluid flow interact with an elastic structure, leading to amplified oscillations. This interaction creates a positive feedback loop: the structure’s deflection alters the aerodynamic forces, which in turn further deflect the structure. If the energy input from the aerodynamic forces exceeds the structure’s damping capacity, the oscillations can grow uncontrollably, resulting in flutter. This instability typically arises when bending and rotational motions occur simultaneously, as seen in the coupled pitching and plunging modes of an aircraft wing. Various structures, including aircraft wings, bridges, and even stop signs, can experience flutter. To study this phenomenon mathematically, researchers often use models like the Euler–Bernoulli beam theory, which in this case incorporates nonlinear curvature to capture the complexities of large deflections, as outlined in [1]. When this beam is exposed to an external harmonic force near its natural frequency and a particular fluid flow, it exhibits self-excited vibrations. The fluid flow is modeled with non-linear damping, which includes a negative linear component similar to Rayleigh’s damping function. Rather than dissipating energy, this negative damping injects energy