Vibration energy transfer and dissipation in impact oscillators with friction

We investigate the vibrational energy transmission and dissipation of energy in mechanical jointed systems using single degree-of-freedom (DOF) and 2DOF impact oscillators incorporating dry friction. Analytical and semi-analytical harmonic balance methods (HBM) are employed to evaluate dynamic responses, transmissibility, and power flow indices, with results validated via numerical integration. In the single-DOF system, friction increases force transmissibility and input energy in the non-impact regime, while enhancing dissipation and reducing transmission in the impact regime. In the 2DOF coupled system, dry friction at the interface induces stick-slip behaviour and energy transfer fluctuations, especially at low frequencies. A distinct superharmonic resonance peak emerges when impact oscillators begin to engage. The interactions between dry friction and the elastic impact constraint are frequency-dependent and competitive: lower friction facilitates constraint engagement and energy transfer at low frequencies, whereas higher friction reduces transmission and promotes localized energy dissipation near resonance. Non-monotonic features in the power-flow indices reveal that optimal combinations of dry friction and impact constraint parameters exist for minimal energy transfer or dissipation across the coupled non-smooth interface. The study reveals vibration transmission mechanisms in jointed systems with frictional sliding and intermittent impacts. It demonstrates that well tuned dry friction and elastic constraints can serve as effective passive vibration control elements in systems with clearance and frictional nonlinearities.