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.

受袋鼠身体运动的启发，对包含三个单元的多自由度振动隔离平台进行了建模，即受保护物体，非线性能量吸收体和X形结构，并且该系统的方程以统一的相对坐标的形式给出。此外，通过谐波平衡和Runge-Kutta算法支持位移传递性分析和数值计算，结果表明：（a）时频响应中存在非线性行为和共振现象；（b）准周期性运动可能是周期性稳态响应或强共振的预测因子，准周期运动之前的位移演化可以用来区分这两种现象。此外，基于数值方法，讨论了选定频率下的系统能量变化。最后，通过Adams中的仿真数据验证了理论分析的正确性。综上所述，这些结果表明，动态特性在特定频带中的结构参数是可调整的和可设计的，并且可以为降低实际工程应用中的共振峰的幅度并提高隔振性能提供有用的方法。