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Experimental research on vibration control of composite plate with piezoelectric networks
LI Lin , SONG Zhiqiang , YIN Shunhua , LI Chao
Collaborative Innovation Center for Advanced Aero-Engine, School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-08-04; Accepted: 2015-09-25; Published online: 2015-10-08 18:25
Corresponding author. LI Lin, Tel.:010-82313998, E-mail:feililin@buaa.edu.cn
Abstract: The paper mainly studies the vibration control of the plate with piezoelectric network. After giving the dynamic equations of the plate with piezoelectric network based on the homogeneous assumption, we resolved the problem that the necessary inductance in the network is too large to be realized in practice. Two kinds of simulated inductance circuit are designed. The respective vibration control effect and characteristic of the composite plate with two kinds of piezoelectric network, that is, the network only with resistors and that with resistors and inductors, are compared experimentally. Experiments prove that the electromechanical coupling dynamic equations based on the homogeneous assumption can well predict the dynamic characteristics of the plate with piezoelectric network. The coupling relationship between electrical modes and mechanical vibration modes of piezoelectric composite plate is also verified. A suggestion for determining the optimal electrical parameters to have a good effect of vibration suppression is given, which can be used as a reference for practical design of the composite plate with piezoelectric network.
Key words: piezoelectric network     vibration control     experimental verification     electromechanical coupling     homogenization

1 压电网络复合板模型及频率响应函数 1.1 机电耦合动力学方程

 图 1 压电网络及复合板的连接 Fig. 1 Connection of composite plate with piezoelectric network
 图 2 压电片的电路连接方式 Fig. 2 Circuit connected way of piezoelectric patch

 图 3 压电片之间的电路形式 Fig. 3 Circuit patterns between piezoelectric patches

 (1)

1.2 方程的求解

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

Bkm的模表示压电网络复合板第k阶机械场频率响应幅值，将求解的式(8)代入式(2)即可求解压电网络复合板在任意频率下的频率响应。由推导过程和式(10)可知，当同阶模态下电路谐振频率与压电复合板共振频率接近时，压电网络能够对薄板进行振动控制。

2 实验装置、测试方法及模拟电感电路 2.1 实验装置

 图 4 计算机、OROS振动信号分析仪和电压放大器 Fig. 4 Computer, OROS vibration signal analyzer and voltage amplifier
 图 5 PEMP、激振器和加速度传感器 Fig. 5 PEMP, actuator and acceleration sensors

 图 6 压电网络电路 Fig. 6 Circuits of piezoelectric network

 材料参数 数值 尺寸/mm 40×40×0.5 数量 3×3 密度/(kg·m-3) 7 800 介电常数εS33/(10－8F·m-1) 1.593 压电系数d31/(10－10C·N-1) -1.85 实测电容值/nF 89

2.2 测试方法

 (11)

1) 线性扫频速度条件：Smax < 216f r2ξr2 Hz/min，frξr分别为共振频率和模态阻尼。

2) 对数扫描速度条件：Smax < 310f r2ξr2 Oct/min。

 参数 采样频率/Hz 采样时间/s 扫频范围/Hz 扫频速度/(Hz·s-1) 数值 1 024 655 10~410 0.605 6

2.3 模拟电感电路

 图 7 里奥登模拟接地电感电路图 Fig. 7 Circuit diagram of Riordan's simulated grounded inductance

 (12)

 图 8 模拟的浮地电感电路 Fig. 8 Simulated floating inductive circuit

 (13)

 图 9 电流传输器CCⅡ Fig. 9 Second generation current conveyors (CCⅡ)

 (14)

 图 11 模拟电感电路 Fig. 11 Simulated inductive circuit

 电感类型 参数 参数数值 等效电感值Leq/H 接地电感 R1/kΩ 1 0.03R2 R3/kΩ 1 R4/kΩ 30 C/μF 1 浮地电感 R3/kΩ 30 0.03R2 C/μF 1

3 实验结果与讨论

3.1 R-PEMP实验结果

 图 12 R-PEMP的频率响应测试曲线 Fig. 12 Test curves of frequency response of R-PEMP
 图 13 R-PEMP的理论及实验频率响应曲线 Fig. 13 Theoretical and experimental curves of frequency response of R-PEMP
3.2 LR-PEMP实验结果

 图 14 LR-PEMP的理论与实测频率响应曲线 Fig. 14 Theoretical and measured curves of frequency response of LR-PEMP

3.3 振动抑制效果的改善

 图 15 R-PEMP与压电网络的实验频率响应曲线 Fig. 15 Experimental curves of frequency response of R-PEMP and piezoelectric network

 压电复合板模态 电路模态 实测频率响应曲线共振峰阶数 复合板共振频率/Hz 振型(实验) 电路网络谐振频率/Hz 振型(理论) 1 58 (1, 2) 61 (1, 1) 2 93 (2, 2) 92 (1, 2) 3 111 115 (2, 2) 4 146 136 (2, 3) 5 150 152 (3, 3)

 图 16 最优参数下的频率响应曲线 Fig. 16 Frequency response curves with optimal parameters
3.4 R-PEMP和LR-PEMP减振效果比较

 图 17 LR-PEMP与R-PEMP减振效果的对比 Fig. 17 Comparison of vibration suppression effect between LR-PEMP and R-PEMP

R-PEMP和LR-PEMP取得最优减振效果时的电阻值不同。当2种类型的PEMP的电阻均为最优电阻时(分别为R=100 kΩ和R=1 MΩ)，其频率响应曲线如图 18所示，通过比较可知，最优参数下，LR-PEMP的减振效果(75%)也要明显优于R-PEMP(35%)。故LR-PEMP相对于R-PEMP更具有实际应用价值。

 图 18 LR-PEMP和R-PEMP最优参数下的减振效果对比 Fig. 18 Comparison of vibration suppression effect between LR-PEMP and R-PEMP with optimal parameters
4 结论

1) 基于均质化的PEMP机电耦合动力学方程能够较好地刻画压电网络PEMP的动力学特性，可以用于分析电学参数对PEMP减振效果的影响规律。

2) R-PEMP具有多模态振动控制效果，对电阻值参数不敏感，但是减振效果有限。

3) LR-PEMP可以针对薄板某阶振动取得最佳振动控制效果，且随着电感的增大，最佳振动控制频带向低频移动；LR-PEMP减振效果要明显优于R-PEMP。

4) LR-PEMP针对某阶共振取得最优振动控制效果的电学参数是使同阶模态下的电路谐振模态信息(包括频率和振型)与压电复合板的同阶模态信息一致的参数。

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文章信息

LI Lin, SONG Zhiqiang, YIN Shunhua, LI Chao

Experimental research on vibration control of composite plate with piezoelectric networks

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(8): 1557-1565
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0514