LAUSR

The paper mainly presents the dynamical characteristics of a base-excited viscoelastic isolation system with real-power geometric nonlinearities under a delayed PPF controller. This controller is coupled to the main system with 1:1 internal resonance. Firstly, the perturbation method of multiple scales is adopted to explicitly find the coupled relationship of the frequency response equations. The results demonstrate that under over-linear restoring force, the amplitude–frequency responses of the viscoelastic isolation system are of the hardening type, which only appears on the right branch of the double-peak response. In this respect, increasing the detuning parameter of the controller results in the appearance of frequency island phenomenon on the right branch of the double-peak response, while the amplitude of the controller degenerates into the traditional single-peak response along with the frequency island. Then, it is worth noting that the vibration can be suppressed effectively by the viscoelastic damping parameters. Furthermore, eight types of interesting dynamical response phenomena are found with the change in time delays under different excitation amplitudes. To this end, the stability analysis, showing the performance of the controller strategy, is carried out by combining the response characteristics. Finally, from the perspective of suppressing the peak amplitude and maintaining the resonance stability, the suitable feedback gains and time delays are determined by means of frequency responses as well as stability conditions.