Vibration transmission and power flow in impact oscillators with linear and nonlinear constraints

This paper investigates the vibration transmission and power flow behaviour of impact oscillators comprising linear or quasi-zero-stiffness (QZS) nonlinear constraints. The steady-state responses of the systems subjected to a harmonic excitation are obtained by the harmonic balance (HB) approximations and numerical integrations. The level of vibration transmission within the systems is quantified by the force transmissibility and time-averaged power flow variables. The effects of the stiffness and damping properties of the constraints on the dynamic response and the vibration transmission are investigated and compared. For a single-degree-of-freedom (SDOF) impact oscillator with a linear constraint, it is found that high constraint stiffness may reduce the response amplitude but lead to high force transmission to the constraint. For a two-degree-of-freedom (2DOF) impact oscillator with a linear constraint at the coupling interface, there may be three peaks in the curves of the relative displacement between the masses and also in those of the force transmissibility to the secondary mass. The addition of the constraint may also result in significantly larger amount of the time-averaged dissipated power at the interface. A higher spring stiffness of the linear constraint can increase the peak values of the relative displacement and force transmissibility to the secondary mass, but may reduce the time-averaged transmitted power to the secondary oscillator. The nonlinear constraint can be designed to tailor the magnitude of force transmissibility and the amount of power flow transmission within impact oscillators, comparing with those of the corresponding linear constraint case. The study provides some enhanced understanding of the influence of stiffness and damping properties of linear and nonlinear constraints on vibration transmission, and benefits dynamic designs of impact oscillators for better performance.