Vibration Control and Parameter Optimization of a Dynamic Vibration Absorber with Inerter and Negative Stiffness

Abstract This study presents a systematic investigation into the vibration control and optimal design of a dynamic vibration absorber (DVA) equipped with an inerter and grounded negative stiffness. A combined approach integrating classical optimization theory and intelligent algorithms is adopted. Based on fixed-point theory (FPT), optimal analytical expressions for key parameters are derived, providing a solid theoretical foundation for subsequent multi-parameter optimization via intelligent algorithms. Furthermore, the particle swarm optimization (PSO) algorithm is employed to achieve approximately equal peak amplitudes at the two resonant frequencies in the amplitude-frequency response curve. Comparative simulations with several conventional DVA models demonstrate that, under harmonic excitation of the primary system, the proposed model significantly reduces resonance peaks, enhances system stability, and improves vibration attenuation performance. This work offers both theoretical insights and algorithmic tools to support parameter optimization and practical engineering applications of DVAs.