Vibration control of nonlinear Absorber–Isolator-Combined structure with time-delayed coupling

• Propose a novel Absorber–Isolator-Combined structure for isolation improvement.
• Utilize time delay to adjust the frequencies in different modes into integer ratio for internal resonances.
• Illustrate the control mechanism of vibration suppression for weak and strong internal resonances.
• Utilized the combined effect of time delay and nonlinearity of the system in vibration control.

A nonlinear combined structure consisted of isolator and absorber with time-delayed coupling active control is proposed in this study, whose vibration suppression effectiveness and control mechanism are investigated. The mathematical model of the combined structure is obtained and stability analysis for different structural parameters and time delay are firstly carried out, which provides a general guideline for the ranges of active control parameters. Then the combined effect of nonlinearity and time delay on vibration suppression and energy transfer is discussed in details based on the analysis of control mechanism by the method of multiple scales. Since the time-delayed nonlinear absorber can induce internal resonance between different modes, the vibration energy at low frequencies can be transferred to high frequency mode and the vibration of the fundamental frequency range is thus suppressed. This paper provides a novel application of internal resonance in vibration suppression of an Absorber–Isolator-Combined structure.