The nonlinear integral resonant controller (NIRC) is implemented and analyzed to control the vibration of a viscoelastic isolation system under harmonic excitation. The NIRC consists of a first-order resonant integrator, which provides additional damping in the closed-loop system to reduce the high-amplitude vibration near the resonance frequency. The method of multiple scales is applied to analytically find the relationship of the amplitude–frequency response of the viscoelastic isolation system. Besides, the equation of the backbone curve satisfied is derived. Meanwhile, the suppression performance is verified based on time-domain analysis. It is found that the NIRC can effectively suppress vibration and improve stability of the viscoelastic isolation system. Furthermore, the influence of the detuning parameters, the real-power exponent, the viscoelastic damping, and the external excitation amplitude on the stability regions is investigated. Overall, the vibration reduction mechanism of the NIRC on the viscoelastic isolation system is revealed.
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