连续可调行星齿轮超材料非线性动力学

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关键词：力学超材料；行星齿轮；非线性动力学；吸引域

中图分类号：TB34

DOI：10.3969/j.issn.1004-132X.2025.11.005

Abstract：A continuous steady-state metamaterial with tunable mechanics was designed based on planetary gears.The excelent tunable mechanics properties of metamaterials were studied，which showed the designed metamaterials had a wide range of programmable stiffness and a significantly tunning band gap. The configuration relationship between tunability and structural parameters was analyzed. Then，a rigid-flexible coupling nonlinear dynamics model of planetary gear metamaterials was established and the dynamics characteristics of planetary gear metamaterials were explored by numerical simulation in the processes of dynamic tunning. Moreover，the influences of the system dynamic parameters on the bifurcation characteristics and stability were explored under coupling excitations，and the distribution characteristics of the system vibration response with the coupling parameter plane were disclosed.Finally，an improved noniterative cell mapping method was used to analyze the dependence of the vibration response of the system on the initial conditions. The results show that the planetary gear metamaterials have a wide range of stifness tunability and significantly variable band gap interval.Under the influences of internal and external excitations，the system exhibits various dynamics characteristics.The dynamics characteristics offlexible constructionare mainly affected by structural parameters，and the dynamics characteristics of rigid construction are affected by multiple sets of coupling parameters and initial conditions.

Key words：mechanics metamaterial; planetary gear; nonlinear dynamics；attractive domain

0 引言

力学超材料自提出至今，学者们已围绕仿生、折纸、手性等开展了大量研究工作[1-3]，在此基础上，通过对单元结构与尺寸进行优化，具备改进力学性能的超材料展现出了重大的工程应用前景。（剩余11349字）