Nonlinear inertia and its effect within an X-shaped mechanism – Part I: Modelling & nonlinear properties

This paper presents new understanding and development related to nonlinear inertia and its influence in coupling with an X-shaped anti-vibration 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 inertial design 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 beneficial effects consequently incurred are explored. The results of this study unveil that: (a) There are 3 different typical nonlinear inertia forms while the U-shaped symmetrical nonlinear inertia coupling with X-shaped mechanisms can provide better vibration isolation performance at low frequency, however two other asymmetrical types can have relatively smaller high-frequency transmissibility; (b) High-frequency transmissibility can be tuned to different level, indicating a tunable band-suppress property, which is a unique property discovered in this study; (c) The nonlinear inertia can have stronger and more adjustable nonlinearity and larger inertia range, which lead to very favorite dynamic properties, including (i) lower and adjustable resonant and anti-resonant frequency and peaks, (ii) sharper decay ratio from the peak value to the anti-peak value, and (iii) different levels high-frequency transmissibility (a unique band suppress property). This study provides new insight into application of nonlinear inertia in various engineering systems for better and passive vibration suppression or isolation.