Nonlinear inertia and its effect within an X-shaped mechanism – Part II : Nonlinear influences and experimental validations

In this study, the effects of nonlinear inertia are further investigated and verified with prototyping and experimental validation. The new inertia unit integrated within a well-designed X-shaped mechanism can produce 3 different typical nonlinear inertia forms which have different nonlinear influence on dynamic response. A critical parametric indicator (Ratio of Inertia) is thus proposed to identify and indicate different types of nonlinearities and a new performance assessment indicator (F-stability) is proposed to assess the performance improvement compared to different nonlinearity with respect to linear counterparts in a dynamic excitation sense. A method for testing different nonlinear inertia is also proposed. It is uniquely revealed that (a) the Ratio of Inertia can be well used to tune different types of inertia nonlinearities; (b) the symmetrical nonlinear inertia (HCHE-type) is generally better in vibration isolation with smaller peak/anti-peak values, peak/anti-peak frequencies (∼ 1 Hz and 3∼4 Hz in our prototype), and faster decay rate (∼ -50dB/Dec with our prototype) but higher high-frequency transmissibility compared to the two asymmetric nonlinearities; (c) the nonlinear inertia contributes significantly to tune the interactive force between vibration source and object in the low frequency range (<10 Hz in our prototype) and obviously helpful and robust to stronger excitations. All the theoretical analysis results are verified with our developed prototype. These results should for the first time provide a comprehensive and in-depth understanding of nonlinear inertia and its effects in different cases and thus definitely shed light on various engineering applications. © 2023 Elsevier Ltd. All rights reserved.