Quantification of vibration force and power flow transmission between coupled nonlinear oscillators

This paper presents a quantitative investigation on the level of vibration force and power flow transmission between linearly coupled nonlinear oscillators. Both analytical and numerical methods are employed for systematic examinations of the vibration transmission associated with hardening, softening and double-well potential stiffness nonlinearities in the oscillators. The method of averaging is employed to obtain analytical formulations of the steady-state frequency-response relationship. Time-averaged power flow variables are formulated and used to quantify vibration input, dissipation and transmission levels associated with both periodic and chaotic responses. It is shown that the stiffness nonlinearities have significant effects on vibration transmission levels near resonance frequencies and in the low-frequency range. It is also shown that when both oscillators are of double-well potential stiffness, the system may exhibit chaotic motions with higher levels of vibration transmission between the oscillators as compared to the corresponding first-order analytical approximations, because of large super-harmonic components in the response. It is found that there may be multiple possible levels of vibration transmission due to co-existing periodic or chaotic responses. It is shown that when comparing the vibration transmission levels of the co-existing stable responses, the use of time-averaged transmitted power and force transmissibility may lead to different evaluation outcomes. These findings provide a better understanding of the effects of stiffness nonlinearities on the vibration transmission which may be maximized or suppressed based on specific design objectives for enhanced dynamic performance.