The impacting vibration absorbers

Impacting vibration absorbers (IVA) and impacting inertial amplifier vibration absorbers (IIAVA) are established in this study to control the vibrations of the single and multiple degrees of freedom systems, i.e. SDOF and MDOF. Further, by incorporating the IVA and IIAVA with the base isolator, two hybrid passive vibration absorbers, namely base-isolated impacting vibration absorbers (BI-IVA) and base-isolated impacting inertial amplifier vibration absorbers, are developed and applied to SDOF and MDOF systems. In order to derive the equations of the motion for controlled dynamic systems, Newton's second law has been employed. The impact between the absorber mass and barrier has been modelled using the "signum" function. The standard linearization method has been used to linearise each nonlinear element of the equations of motion. H2 and H infinity optimization techniques are implemented to determine optimal design parameters analytically. The frequency response function is developed to obtain the dynamic system's responses. Accordingly, each proposed absorber's vibration reduction capacity is determined. For SDOF systems, the optimum IIAVA and BI-IVA have 59.44% and 96.63% more vibration reduction capacities than the optimum IVA. In contrast, the optimum IIAVA and BI-IVA have 46.83% and 96.74% more vibration reduction capacities than the optimum IVA when applied to the MDOF systems. In this paper, each one of the results is mathematically accurate.