Responses and energy transmissibility of a viscoelastic isolation system with a power-form restoring force under delayed feedback control

In this paper, combination of cubic nonlinearity and time delay is designed to improve the performance of a viscoelastic isolation system with a power-form restoring force. By the method of multiple scales, the amplitude-frequency response, stability, backbone curve and energy transmissibility are considered. More specifically, three nonlinear cubic delayed feedback control methodologies are examined: position, velocity and acceleration delayed feedback. It is found that the viscoelastic damping coefficient can induce multi-valued response, especially 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 equivalent damping and jump avoidance condition are first proposed to interpret the effect of feedback control loop on dynamical behaviors. Furthermore, with the purpose of improving the stability and reducing the vibration, suitable feedback parameter pairs are determined by the frequency response together with stability conditions. Finally, the vibration isolation property is predicted based on energy transmissibility in different cases. Results show that the strategy proposed in this paper is practicable and feedback control parameters are significant factors to alter dynamical behaviors, and more importantly, to improve the isolation effectiveness for the viscoelastic isolation system.