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新型负刚度吸能结构力学特性分析

侯秀慧 吕游 周世奇 朱志韦 张凯 邓子辰

侯秀慧, 吕游, 周世奇, 朱志韦, 张凯, 邓子辰. 新型负刚度吸能结构力学特性分析. 力学学报, 2021, 53(7): 1940-1950 doi: 10.6052/0459-1879-21-083
引用本文: 侯秀慧, 吕游, 周世奇, 朱志韦, 张凯, 邓子辰. 新型负刚度吸能结构力学特性分析. 力学学报, 2021, 53(7): 1940-1950 doi: 10.6052/0459-1879-21-083
Hou Xiuhui, Lü You, Zhou Shiqi, Zhu Zhiwei, Zhang Kai, Deng Zichen. Mechanical properties analysis of a new energy absorbing structure with negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1940-1950 doi: 10.6052/0459-1879-21-083
Citation: Hou Xiuhui, Lü You, Zhou Shiqi, Zhu Zhiwei, Zhang Kai, Deng Zichen. Mechanical properties analysis of a new energy absorbing structure with negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1940-1950 doi: 10.6052/0459-1879-21-083

新型负刚度吸能结构力学特性分析

doi: 10.6052/0459-1879-21-083
基金项目: 国家自然科学基金(11972287, 11872303, 11802150)和陕西省自然科学基金(2020JQ-106)资助项目
详细信息
    作者简介:

    侯秀慧, 副教授, 主要研究方向: 基于稳定性的超材料结构设计. E-mail: houxiuhui@nwpu.edu.cn

    邓子辰, 教授, 主要研究方向: 复杂系统动力学与控制研究. E-mail: dweifan@nwpu.edu.cn

  • 中图分类号: O34

MECHANICAL PROPERTIES ANALYSIS OF A NEW ENERGY ABSORBING STRUCTURE WITH NEGATIVE STIFFNESS

  • 摘要: 负刚度结构作为一种具有广泛应用前景的力学超材料, 在吸能、减振及降噪等领域呈现出显著的优势, 但传统负刚度结构较低的比能吸收效率以及多稳态非自主回弹等特征, 严重限制了其工程应用. 为解决该问题, 通过单胞构型设计, 提出了一种新型可自主回弹的三维负刚度结构. 该结构利用串联的负刚度单胞在加载−卸载过程中, 曲梁胞元的自主反弹, 实现结构循环加载和多次重复利用; 通过凹槽深度设计抑制单胞多稳态的出现, 并且通过调整侧壁厚度, 控制曲梁屈曲模态的形式, 从而增大负刚度临界载荷差值, 实现吸能效率的显著提升. 随后为实现在复杂载荷环境下的高吸能, 对结构尺寸进行梯度设计, 提出了一种梯度负刚度结构, 利用有限元方法比较分析梯度负刚度结构与均匀负刚度结构在不同载荷作用下的吸能效果. 研究结果表明, 该梯度结构因微结构尺寸的不同, 具有不同的负刚度临界载荷最大值, 从而使其在不同的冲击载荷环境下, 在实现自主回弹的基础上, 均呈现出较好的吸能效率. 该新型负刚度结构为振动控制和结构重组等工程应用提供了技术支持.

     

  • 图  1  负刚度单胞力(F)−位移(S)曲线示意图

    Figure  1.  Sketch of force (F)-displacement (S) relation for a negative stiffness cell

    图  2  负刚度结构力($F$)−位移($S$)曲线示意图[1]

    Figure  2.  Sketch of force ($F$) -displacement ($S$) relation for a negative stiffness structure[1]

    图  3  曲梁组件及三维单胞

    Figure  3.  Curved beam module and 3D unit cell

    图  4  归一化的曲梁力−位移关系的几种解[17]

    Figure  4.  Several solutions of the normalized force-displacement relations of curved beams[17]

    图  5  侧壁厚度${t_1}$对曲梁屈曲模态的影响

    Figure  5.  Effect of lateral wall thickness ${t_1}$on the buckling mode of curved beam

    图  6  两端固定曲梁在二阶模态受到抑制后的屈曲模态

    Figure  6.  Buckling mode of a curved beam fixed at both ends after the second-order buckling mode being suppressed

    图  7  不同侧壁厚度(${t_1}$)下单胞的力($F$)−位移($S$)曲线

    Figure  7.  Force ($F$)-displacement ($S$) relation of the unit cell with different lateral wall thicknesses (${t_1}$)

    图  8  $Q,\;{t/L},{{{t_1}}/t}$对结构屈曲模态的影响(${\theta _1}$${t_1} = 2t$时侧向胞壁相对竖直方向的转角)

    Figure  8.  Effects of $Q,\;{t/L},{{{t_1}}/t}$on buckling modes of the new developed structure (${\theta _1}$ represents the angle of the lateral wall relative to the vertical direction when ${t_1} = 2t$)

    图  9  不同$Q$值下, 结构吸收的能量随${t/L}$的变化关系

    Figure  9.  Variation of energy absorption${W_m}$ with ${t/L}$under different shape factors $Q$

    图  10  单胞吸能比值$\eta $随形状因子${Q^{\left( {{\rm{II}}} \right)}}$的变化关系

    Figure  10.  Variation of energy absorption efficiency $\eta $ with different shape factors ${Q^{\left( {{\rm{II}}} \right)}}$

    图  11  周期结构分析模型

    Figure  11.  Analytical models for periodic structure

    图  12  单胞和周期结构在相同冲击速度下的力学响应

    Figure  12.  Mechanical responses of unit cell and periodic structures under the same impact velocities

    图  13  梯度结构负刚度临界载荷比值($D{F_{{\rm{cr}}}}$)随曲梁壁厚比值($\alpha $)的变化关系

    Figure  13.  Variations of negative stiffness critical force ratio ($D{F_{{\rm{cr}}}}$) with the curved beam wall thickness ratio ($\alpha $) for the gradient structure

    图  14  两种结构在不同冲击速度下的屈曲模态

    Figure  14.  Buckling modes of two structures under different impact velocities

    图  15  两种结构在不同冲击速度下的力学响应

    Figure  15.  Mechanical responses of two structures under different impact velocities

    图  16  梯度单胞结构A与均匀单胞结构B的力−位移曲线

    Figure  16.  Force-displacement relations for gradient cell structure A and uniform cell structure B

    图  17  重组多单元负刚度结构

    Figure  17.  Reassembled multi-element negative stiffness structure

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出版历程
  • 收稿日期:  2021-03-01
  • 录用日期:  2021-05-24
  • 网络出版日期:  2021-05-25
  • 刊出日期:  2021-07-18

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