Vibration control and suppression, as a critical branch of dynamic system research, plays a vital role in ensuring the safety, reliability, and precision of key equipment in aerospace, transportation, and high-end instrumentation. Grounded in an interdisciplinary foundation spanning applied mathematics, engineering mechanics, and materials science, this study investigates the multi-parameter optimization of an inerter-based vibration absorber incorporating a negative stiffness element and a parallel structural configuration. To systematically enhance the absorber’s vibration attenuation performance and dynamic stability, the proposed approach integrates classical analytical theory with intelligent optimization algorithms. First, based on Fixed-Point Theory (FPT), analytical expressions for the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio are derived, thereby establishing reasonable parameter iteration ranges for subsequent intelligent optimization. Due to the highly nonlinear amplitude-frequency response, analytical methods alone struggle to achieve equal-peak optimization. Therefore, Particle Swarm Optimization (PSO) is employed to conduct coordinated multi-parameter optimization. This method aligns the two resonance peaks, thereby achieving the equal-peak condition and broadening the vibration attenuation bandwidth. Comparative analysis with several typical vibration absorber models confirms that the proposed structure exhibits superior vibration mitigation efficiency and stability under external excitation. These research findings offer novel insights into the design and performance optimization of composite systems incorporating inerters and negative stiffness elements, and provide theoretical and technical support for intelligent multi-parameter optimization in complex mechanical systems.
Cui et al. (Tue,) studied this question.