关键词：机械超结构；齿轮元胞；力学性能；连续可调；减振结构

中图分类号：TB34

DOI：10.3969/j.issn.1004-132X.2025.04.023 开放科学（资源服务）标识码（OSID）：

Continuous Multi-stable Gear Cell Mechanical Metastructures and Mechanics Properties

MO Shuai1，2，3 * HUANG Xuan1，² HUANG Zurui1，² ZHANG Wei1 1.State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures，Nanning，530004 2.School of Mechanical Engineering，Guangxi University，Nanning，530004 3.State Key Lab of Digital Manufacturing Equipment and Technology，Huazhong University of Science and Technology，Wuhan，430074

Abstract： In order to expand the forms of mechanical metastructures and optimize the dynamic adjustment ability of mechanical metastructures，a micro gear unit structure was designed，which was periodicall arranged in a two-dimensional plane to form a metastructure. The structural design principle and stability of the metastructure were analyzed.It is demonstrated that continuous and stable tunable of mechanics properties may be achieved by the designed metastructure. The extensive mechanics properties of this metastructure，including statics and dynamics，were analyzed through finite element simulation method.The results indicate that the elastic modulus of the externall meshed gear cells has a tuning range exceeding 1O times，while that of the internally meshed planetary gear cells exceeds 200 times. A considerable tunable range is also observed in the shear modulus.Additionally，the continuous change of the natural frequency and frequency amplitude curve may be realized by this gear unit-based metastructure，providing a new idea for the design of materials aimed at vibration reduction. Finally，a variety of metastructure vibration reduction devices were designed based on this micro gear unit， demonstrating the unique advantages and broad application prospects in vibration reduction and dynamic control.

Key words： mechanical metastructure; gear cell; mechanics property; continuously tunable； vibration-reduction structure

0 引言

超材料/超结构是具有非常规性能的人工结构[1-3]，机械超结构的发展可以追溯到早期的周期梁、板、蜂窝等结构，通过合理配置与优化这些元素，可以实现负泊松比、低密度、高强度等优异力学性能，如GAO等[4]、CHENG等[5]通过对负泊松比结构进行优化，得到具有增强机械性能的超材料。根据不同的应用场景有望在智能设备、能量吸收、减振降噪等领域取得重大应用前景，如将柔性超材料应用于电子皮肤，能够使机械手臂更加精确地执行抓取任务6；在汽车零部件中引入超材料，能够有效缓解轻量化材料所带来的噪声问题。

随着高精度制造技术的不断开发，机械超结构的力学可调超结构在设计、制造、应用等方面发生快速转变[7-8]，具有易设计、多功能、动态可调的机械超结构受到大量学者的广泛关注，这类超结构通过主动或被动调节使自身可重构[9]，这样的可重塑性使装备机械超结构的设备能够灵活地调节自身刚度，从而可适应多场景任务。ZHANG等[10]设计了一种可再入结构，通过控制其内置的楔形块实现了结构刚度可调；TAO等[11]利用水凝胶的溶胀特性驱动复合结构弯曲，获得了带隙可调的三维力学超材料；区别于上述设计方案，FANG等[12]、MEEUSSEN等[13]利用齿轮元素设计出性能可调的力学超材料，但未从微观结构上进行拓扑优化，同时缺乏动力学特性及其在减振结构设计方面的研究。……