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压电超材料梁中弹性波带隙特性与界面传输的主动控制

孙文静 王毅泽

孙文静,王毅泽. 压电超材料梁中弹性波带隙特性与界面传输的主动控制 [J]. 应用数学和力学,2022,43(1):14-25 doi: 10.21656/1000-0887.420125
引用本文: 孙文静,王毅泽. 压电超材料梁中弹性波带隙特性与界面传输的主动控制 [J]. 应用数学和力学,2022,43(1):14-25 doi: 10.21656/1000-0887.420125
SUN Wenjing, WANG Yize. Active Control on Band Gap Properties and Interface Transmission of Elastic Waves in Piezoelectric Metamaterial Beams[J]. Applied Mathematics and Mechanics, 2022, 43(1): 14-25. doi: 10.21656/1000-0887.420125
Citation: SUN Wenjing, WANG Yize. Active Control on Band Gap Properties and Interface Transmission of Elastic Waves in Piezoelectric Metamaterial Beams[J]. Applied Mathematics and Mechanics, 2022, 43(1): 14-25. doi: 10.21656/1000-0887.420125

压电超材料梁中弹性波带隙特性与界面传输的主动控制

doi: 10.21656/1000-0887.420125
基金项目: 国家自然科学基金(11922209;11991031;12021002)
详细信息
    作者简介:

    孙文静(1996—),女,硕士生(E-mail:18121003@bjtu.edu.cn)

    王毅泽(1981—),男,教授,博士(通讯作者. E-mail:wangyize@tju.edu.cn)

  • 中图分类号: O342; TB34

Active Control on Band Gap Properties and Interface Transmission of Elastic Waves in Piezoelectric Metamaterial Beams

  • 摘要:

    该文采用周期压电负电容电路,研究了弹性波超材料梁中带隙特性的主动控制问题。该系统利用外部电路改变所连接压电材料的材料参数,从而改变结构的等效参数,实现对带隙特性的调控。通过对单胞进行控制,可观察到主动控制系统作用时带隙的产生与消失。构造了含有交界面的弹性波超材料梁结构,分析了主动控制系统对波动界面传输特性的影响。

  • 图  1  压电分流结构单胞

    Figure  1.  The unit cell of the piezoelectric circuit

    图  2  具有不等厚度压电片的主动弹性波超材料梁

    Figure  2.  Active elastic wave metamaterial beam attached by piezoelectric patches with different thicknesses

    图  3  含有负电容电路的主动控制系统

    Figure  3.  The active control system with a negative capacitance circuit

    图  4  变形关系:(a)超材料梁的变形;(b)节点的位移

    Figure  4.  The deformation relation: (a) the deformation of the layered elastic-piezoelectric beam; (b) the displacements of the nodes

    图  5  压电片对称粘贴但厚度改变时弹性波超材料梁的局部化因子

    Figure  5.  The localization factors of the elastic metamaterial beam with different-thickness piezoelectric sheets symmetrically pasted

    图  6  上下层压电片厚度相同与不同时弹性波超材料梁的局部化因子

    Figure  6.  The localization factors of the elastic metamaterial beam with the same- and different-thickness piezoelectric patches

    图  7  弹性波超材料梁有无主动控制时的局部化因子

    Figure  7.  The localization factors of the elastic metamaterial beam with and without active control

    图  8  实验装置:(a)数据采集仪(上)和信号放大器(下);(b)信号发生器;(c)实验模型;(d)电路实物图;(e)压电片细节图

    Figure  8.  The experimental equipment: (a) the data acquisition instrument (upper) and the signal amplifier (lower); (b) the signal generator; (c) the experimental model; (d) the physical circuit diagram; (e) the detailed diagram of the piezoelectric patch

    图  9  传输响应:(a) 3 850 Hz,主动控制前;(b) 3 850 Hz,主动控制后;(c) 5 659 Hz,主动控制前;(d) 5 659 Hz,主动控制后

    Figure  9.  Transmission responses: (a) at 3 850 Hz before active control (b) at 3 850 Hz after active control; (c) at 5 659 Hz before active control; (d) at 5 659 Hz after active control

    图  10  激励端和接收端的响应值:(a) 3 850 Hz,主动控制前;(b) 3 850 Hz, 主动控制后;(c) 5 659 Hz,主动控制前;(d) 5 659 Hz,主动控制后

    Figure  10.  The responses at the excitation and the receiving end: (a) at 3 850 Hz, before active control; (b) at 3 850 Hz, after active control; (c) at 5 659 Hz, before active control; (d) at 5 659 Hz, after active control

    图  11  结构能带图

    Figure  11.  The band structure

    图  12  响应图

    Figure  12.  The response diagram

    图  13  弹性波幅值响应图

    Figure  13.  The diagram of elastic wave responses

    图  14  实验模型

    Figure  14.  The experimental model

    图  15  激励端和接收端的响应值:(a)主动控制之前的实验结果;(b)经过主动调控之后的实验结果

    Figure  15.  The responses at the excitation and the receiving end: (a) experimental results before active control; (b) experimental results after active control

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出版历程
  • 收稿日期:  2021-05-07
  • 录用日期:  2021-05-17
  • 修回日期:  2021-08-30
  • 网络出版日期:  2021-12-18
  • 刊出日期:  2022-01-01

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