Global Admittance: A New Modeling Approach to Dynamic Performance Analysis of Dynamic Vibration Absorbers

The vibration control in structural design has long been a critical area of study, particularly in mitigating undesirable resonant vibrations using dynamic vibration absorbers (DVAs). Traditional approaches to tuning DVAs have relied on complex mathematical models based on Newtonian or Euler–Lagrange equations, often leading to intricate systems requiring simplification of the analysis of multi-degree-of-freedom structures. This paper introduces a novel modeling approach for analyzing DVAs based on the concept of global admittance, which stems from mechanical admittance and network simplifications. This model streamlines the representation of structures with DVAs as one-degree-of-freedom systems coupled with a global admittance function, which emulates additional damping coupled to the primary structure. In this work, global admittance functions are determined by the independent analysis of the mechanical networks of the DVA, restructuring the process of obtaining the system’s transfer function. The model was validated using different classical DVA configurations, demonstrating total accuracy in its applicability across designs concerning conventional modeling. Our most remarkable finding was that the dimensionless function, 𝛾g (Ω), resulting from the global admittance, partially decouples the dynamics of the DVAs from the primary structure, facilitating the implementation of passive vibration control strategies in more realistic structural models. Additionally, this work establishes a significant advancement in vibration control analysis, providing a flexible tool for control strategies in real-world structural systems.