Vibration is a critical issue in aerospace structures, where lightweight design, high flexibility, and complex operational environments often lead to pronounced nonlinear dynamic responses. Excessive vibrations induced by harmonic excitations, aerodynamic loads, or onboard equipment can significantly degrade structural integrity, control accuracy, and service life. Consequently, advanced passive vibration suppression techniques with strong robustness and broadband effectiveness are of great importance in aerospace engineering applications. The bifurcation boundary and vibration suppression performance of Piezoelectric–Monostable Nonlinear Energy Sink (PMNES) are crucial for evaluating its effectiveness on the main structure. To simplify the analysis of flexible aerospace structures, a reduced-order model is derived by modal truncation in the low-frequency range, which is then treated as a two-degree-of-freedom main structure. To focus on the underlying nonlinear dynamic mechanisms, an equivalent two-degree-of-freedom lumped-parameter system is adopted as a generic representation of the dominant low-frequency dynamics of flexible aerospace structures. In this work, the electromechanical coupling control equations of the system of a two-degree-of-freedom main structure coupled with PNES are derived through the application of Newton’s second law and Kirchhoff’s voltage law. The methods of complexification-averaging (CX-A) and Runge–Kutta (RK) are employed to assess the vibration suppression performance and stability characteristics of the system under harmonic excitation. The approximate solution is validated through numerical solutions. The approximate solutions of the system are employed to derive the Saddle Node (SN) bifurcation and codimension-two cusp bifurcation points, while the enhanced algorithm is employed to ascertain the most unfavorable amplitude at each external excitation circular frequency and to determine whether the mark represents a Hopf Bifurcation (HB) point. The generalized transmissibility is utilized to assess the efficacy of vibration suppression. The various vibration suppression efficiency regions are created by superimposing the vibration suppression efficiency maps and bifurcation maps. The influence of PNES parameters on the vibration suppression region is investigated. The results indicate that this method can effectively evaluate the bifurcation boundary and vibration suppression performance of PMNES.
Yang et al. (Tue,) studied this question.