Vibration transmission and power flow in nonlinear smooth and non-smooth dynamical systems - DAI, WEI (2020)
Vibration power flow analysis (PFA) approach has been widely used as a tool for investigating the dynamic behaviour of coupled structures and complex systems. There have been numerous PFA studies on linear systems; however, limited research has been reported on the power flow behaviour of nonlinear systems, especially on the nonlinear non-smooth systems. This research attempts to address the issue by seeking a deeper understanding of the effects of smooth and non-smooth nonlinearities on vibration transmission and power flow in nonlinear dynamical systems, and for an improved design of nonlinear isolation structures to obtain better vibration mitigation performance based on the findings from PFA. The vibration transmission characteristics of non-smooth impact oscillators with linear constraint and different types of geometrically nonlinear motion constraints are firstly investigated. It is shown that the inclusion of nonlinear motion constraint can lead to a higher proportion of the input power dissipated at the interface compared to that of the linear constraint. The nonlinear constraints can be designed to tailor the level of force transmission and vibration power flow near the peak frequencies. The use of force transmissibility and time-averaged power flow as measures of the vibration transmission level may result in different evaluation outcomes. Nonlinear constraint can lead to bifurcations as well as super-harmonic and sub-harmonic response components. Secondly, the vibration mitigation performance of a nonlinear isolation system with a geometrically nonlinear element based on linkage mechanism is studied. It is found that the addition of the nonlinear element to a linear isolator can enlarge the effective isolation frequency range and bring about softening effect on the system. The curves of frequency response, force transmissibility and power transmission are shifted to the low-frequency range and the peaks of the curves can bend to the low frequencies with possibly reduced peak values. Thirdly, the dynamic behaviour of the non-smooth friction oscillators is explored from the vibration energy perspective. It is shown that the discontinuous dry friction nonlinearity can lead to a significant increase in the force transmissibility, energy transfer and energy dissipation at high frequencies, while there are slight reductions in the peak values of these indices. The findings from this study contribute to an enhanced understanding of vibration transmission and power flow characteristics within both smooth and non-smooth nonlinear dynamical systems and assist dynamic design of engineering systems for better performance.