Active Control on Band Gap Properties and Interface Transmission of Elastic Waves in Piezoelectric Metamaterial Beams
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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。
Abstract:The active control on band gap properties of elastic wave metamaterial beams was studied by means of the negative capacitance circuits attached to piezoelectric sheets periodically. External circuits were used to change the material constants of the connected piezoelectric materials, which could tune the equivalent parameters of the structure and control the band gap characteristics. Through controlling the unit cell, the generation and disappearance of band gaps can be observed with the active control system. Then, an elastic wave metamaterial beam with the interface was constructed to discuss the effects of the active control system on the interface transmission.
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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
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