Vibration control using a quasi-zero stiffness inerter: The tuning approach

Abstract

The use of dynamic vibration absorbers remains one of the most effective methods for mitigating unwanted oscillations in various engineering applications. Nonlinear absorbers, such as those based on Quasi-Zero Stiffness (QZS) and Nonlinear Energy Sinks (NES), offer significant advantages in terms of energy dissipation over a wide frequency range. This paper focuses on a hybrid system composed of a single-degree-of-freedom QZS main structure with an attached NES type inerter absorber. An analytical approach is presented to derive the frequency amplitude relation (FAR), accounting for six key dimensionless parameters that describe the system dynamics. Although the general expression for FAR is complex, for a given mechanical configuration of the main structure, it becomes feasible to determine the optimal damping coefficient and nonlinear stiffness of the absorber using a straightforward analytical-numerical method. The practical absence of linear stiffness components enables the absorber to operate efficiently under external harmonic excitation. Numerical integration of the system’s equations of motion demonstrates strong agreement with theoretical predictions and confirms the effectiveness of the proposed tuning methodology in suppressing vibrations.