Amplitude–Frequency Response Characteristics and Parameter Optimization of a Bistable Nonlinear Energy Sink Under Wide-Frequency Harmonic Excitation

To address the detuning sensitivity of conventional linear vibration absorbers under wide-frequency harmonic excitation and the limited effectiveness of nonlinear energy sinks (NESs) in low-energy regimes, this study investigates a bistable nonlinear energy sink (BNES) based on a negative-stiffness support. A coupled model of the primary system and the BNES is established, and the analytical steady-state amplitude-frequency relationship of the system is derived using the harmonic balance method. The accuracy of the analytical solutions is verified through numerical integration. Based on the first Lyapunov method, the instability regions of the system are identified, and the effects of system parameters on the amplitude-frequency response of the primary structure are analyzed. On this basis, a comprehensive performance index that accounts for both peak suppression and average vibration reduction over the frequency band is constructed, and an improved particle swarm optimization algorithm is employed for parameter optimization. The results demonstrate that the optimized BNES can effectively suppress isolated high-amplitude response branches and significantly reduce the response of the primary system within the resonance frequency band, exhibiting superior broadband vibration mitigation performance and enhanced stability.