Vibration transmission and energy flow of impact oscillators with nonlinear motion constraints created by diamond-shaped linkage mechanism

This study investigates the dynamic behaviour and vibration transmission of impact oscillators with nonlinear motion constraints. The proposed nonlinear motion constraint with geometric stiffness nonlinearity is created by a linear spring embedded in a diamond-shaped linkage mechanism (DSLM). The harmonic balance (HB) approximations and numerical integrations are both employed to obtain the steady-state response of the systems subjected to harmonic force excitations. The force transmissibility and time-averaged power flows are used as indices to quantify and evaluate the vibration transmission and dissipation in impact oscillators. For a single-degree-of-freedom (SDOF) impact oscillator, it is found that the use of the nonlinear constraint can lead to a higher response amplitude but a substantially lower force transmissibility than those of the corresponding linear constraint case. For a two-degree-of-freedom (2DOF) impact oscillator, an extra peak is found in the curves of relative displacement between masses and in those of the force transmissibility to the secondary mass, while a local minimum point may exist near the extra peak. The inclusion of nonlinear motion constraint can lead to a higher proportion of the input power dissipated at interface compared to the linear constraint case. It is shown that the level of vibration power flow transmission within impact oscillators can be tailored by adjusting design parameters of the nonlinear constraint. It is also found that the nonlinear constraint may lead to bifurcations as well as super-harmonic and sub-harmonic response components. The findings from the study provide an in-depth understanding of the effects of design parameters and locations of nonlinear constraints on the vibration transmission in impact oscillators and assist in superior dynamic design of such systems for desirable vibration performance.