This paper analyses the nonlinear inertia and its effect in coupling with an X-shaped anti-vibration mechanism in more depth based on the proposed novel inertia design mechanism. The inertia unit is designed with an inspiration from arm swing of human body in walking and integrated within an anti-vibration X-shaped mechanism. The new mechanism allows larger excitation displacement and more adjustable inertial ratio compared to previous designs, resulting in much more reduced vibration transmissibility and resonant peak and also producing both symmetric and asymmetric nonlinear inertia. The research results unveil that: (a) the Ratio of Inertia can be well used to tune different types of inertia nonlinearities; (b) The U-shaped symmetrical nonlinear inertia can provide better anti-vibration performance at low frequency; (c) High-frequency transmissibility can be tuned to different level, indicating a tuneable band-suppress property, which is a unique property discovered in this study; (d) the nonlinear inertia contributes significantly to tune the interactive force between vibration source and object in the low frequency range and obviously helpful and robust to stronger excitations. This study provides new insights into the application of nonlinear inertia in various engineering systems to achieve better passive vibration suppression.

This study evidence that the resonant phase lags found numerically and analytically for single-degree-of-freedom systems in Volvert et al. cannot always be extended to the multi-degree-of-freedom case. Indeed, the potential interactions between primary and secondary resonances have a direct influence on the evolution of the phase lag of the studied harmonic. A phase lag that is a combination of carefully selected harmonics, should be considered to remove the influence of the other harmonics.