Dynamical properties of a forced vibration isolation system with real-power nonlinearities in restoring and damping forces

In this paper, the time-delayed cubic velocity feedback and the real-power form of restoring and damping forces are combined to improve the performance of vibration isolation. The primary resonance, dynamic stability and transmissibility are studied for a forced vibration isolation system with real-power exponents in restoring and damping force terms under base excitation. Based on the method of multiple scales, the equivalent damping is first proposed to interpret the effect of feedback control on the dynamic behavior of the real-power isolation system, such as the frequency island phenomenon. In this regard, the isolation system indicates the softening behavior for under-linear restoring force and hardening behavior for over-linear restoring force. And multi-valued responses, especially five-valued responses, are found under under-linear restoring force. To verify this result, the stability boundaries are characterized and presented excellent agreement with the responses. Then, for avoiding the jump phenomenon, an analytical criterion is derived and confirmed by the numerical simulation. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gains and time delays are derived. Finally, the effects of the system parameters on the energy transmissibility is investigated. Results show that the strategy proposed in this paper is practicable and feedback parameters are significant factors to improve the isolation effectiveness for the real-power isolation system.