Nonlinear vibrations of flexible structures in viscous flow arise from strong interactions among vortex shedding, structural geometric nonlinearity and modal competition, particularly at high Reynolds numbers where multiple instability mechanisms coexist. These interactions can lead to subharmonic bifurcations, higher-mode-dominated large-amplitude oscillations and intermittent dynamics. In this work, a strongly coupled fluid–structure–electro–control computational framework is developed to investigate the nonlinear vibration of a piezoelectric beam behind a circular cylinder in viscous flows. The incompressible Navier–Stokes equations are solved within an arbitrary Lagrangian–Eulerian (ALE) formulation and fully coupled with a geometrically nonlinear piezoelectric beam model. A unidirectional circuit is introduced to realize local self-sensing and adaptive actuation. Numerical results show that at Re = 500 the uncontrolled system exhibits large-amplitude responses dominated by subharmonic components and second-mode frequencies. Activation of the unidirectional circuit suppresses the subharmonic bifurcation and drives the system towards a stable vibration. At Re = 1000, the interaction between highly unsteady flow structures and localized electromechanical actuation induces a spontaneous intermittent dynamical regime, characterized by recurrent transitions between periodic oscillations and burst-like fluctuations. The study demonstrates that unidirectional circuit control not only stabilizes nonlinear vibrations but also reshapes the underlying dynamical landscape. The proposed computational framework provides a robust tool for analysing fluid–structure systems with coupled electrical and control strategy.