Vibration power flow transmission between nonlinearly coupled oscillators with dual forces excitations

This paper investigates the vibration power flow transmission between nonlinearly coupled oscillators, each subjected to a harmonic excitation force with different phase angles. The harmonic balance method is used for analytical formulations of frequency-response relationship and time-averaged power flows. Numerical integrations are also conducted for validation of the analytical results and for comparison. Time-averaged transmitted power between the oscillators is used as an index to quantify the level of vibration transmission. The effects of the stiffness nonlinearity of the coupling interface on vibration power transmission are studied and revealed. It is found that when the excitation forces are of certain phase difference, the dynamic response of the oscillators and power flow between then may be reduced in the low-frequency range. The relative displacement amplitude between two oscillators may increase with the relative phase angle. It is also found that when the system is excited near resonances, the relative phase angle has little effects on the response amplitudes and time-average input power. It is also shown that time-averaged transmitted power is more sensitive than time-averaged input power to the relative phase angle. These findings lead to better understanding of vibration transmission mechanisms of coupled systems with different excitation forces and thus can facilitate enhanced designs of vibration suppression systems.