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

Abstract

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∼4Hz 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 (<10Hz 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.