Enhancing vibration control: A parallel integration of tuned mass damper with inerter and vibro-impact nonlinear energy sink

Abstract

This study introduces a novel vibration suppression system by combining a Tuned Mass Damper with Inerter (TMDI) and a Vibro-Impact Nonlinear Energy Sink (VI-NES) in a parallel configuration. This configuration enhances the efficiency of the absorbers compared to a series arrangement, which tends to diminish energy reduction efficiency. The dynamic characteristics of this combined system are examined through intricate differential equations that model the motion of both the primary structure and its attached absorbers. Utilizing the method of multiple scales, the study investigates the system's responses to various conditions, including external forces and impacts. A chaotic, strongly modulated response is analyzed both analytically and numerically. The linear oscillator is subjected to an external force, and its dynamic behavior is examined using bifurcation analysis. This analysis aids in identifying the regions where a strongly modulated chaotic response occurs. Findings demonstrate that the integration of TMDI and VI-NES achieves superior vibration suppression compared to each device used independently. The research also delves into how parameters such as restitution coefficient, gap size, inertance, stiffness, and damping coefficient influence the vibrational behavior and energy dissipation efficiency of the system. Additionally, optimal settings for these parameters are identified to maximize the absorbers' performance. The optimal absorber is examined under harmonic forcing using bifurcation analysis. This innovative approach provides a practical and effective solution for vibration control in nonlinear systems using passive devices. © 2025 Elsevier Ltd.