Abstract
Inspired by the body movement of the kangaroo, a multi-degree-of-freedom vibration isolation platform containing three units, that is, a protected object, a nonlinear energy sink, and an X-shaped structure, has been modeled, and the differential equations of the system have been given in the form of uniform relative coordinates. Furthermore, the displacement transmissibility analysis and numerical calculation are supported by the method of harmonic balance and Runge–Kutta algorithm, which shows that (a) there are nonlinear behaviors and resonant phenomenon in the time–frequency response and (b) quasi-periodic motion may be a predictor of periodic steady-state response or strong resonance, and the displacement evolution before quasi-periodic motion may be used to distinguish the two phenomena. In addition, based on the numerical method, the system energy changes in a selected frequency are discussed. Finally, the correctness of the theoretical analysis is verified by simulation data in Adams. Taken together, these results demonstrate that the dynamic characteristics are adjustable and designable of structural parameters in a specific frequency band and can provide a useful way to reduce the amplitude of resonant peaks and improve the vibration isolation performance for practical engineering applications.
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