压电纤维材料驱动下复合板扭曲变形效率分析

李琳; 薛铮; 范雨

doi:10.13700/j.bh.1001-5965.2017.0107

压电纤维材料驱动下复合板扭曲变形效率分析

doi: 10.13700/j.bh.1001-5965.2017.0107

李琳^{1, 2},
薛铮³,
范雨^{1, 2, ,}

1.
北京航空航天大学能源与动力工程学院, 北京 100083
2.
先进航空发动机协同创新中心, 北京 100083
3.
空间物理重点实验室, 北京 100076

基金项目:

国家自然科学基金 51675022

详细信息

作者简介:
李琳女, 博士, 教授。主要研究方向:叶盘结构流致振动、智能结构动力学及振动控制

薛铮男, 博士。主要研究方向:主动复合材料及智能结构设计

范雨男, 博士。主要研究方向:智能结构动力学

通讯作者:
范雨, E-mail:fanyu04@buaa.edu.cn

中图分类号: V214.8
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出版历程
- 收稿日期: 2017-02-28
- 录用日期: 2017-06-09
- 网络出版日期: 2018-02-20

Efficiency of twist deformation of composite plate actuated by MFC

LI Lin^{1, 2},
XUE Zheng³,
FAN Yu^{1, 2
, ,}

1.
School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
2.
Collaborative Innovation Center for Advanced Aero-Engine, Beijing 100083
3.
Science and Technology on Space Physics Laboratory, Beijing 100076, China

Funds:

National Natural Science Foundation of China 51675022

More Information

Corresponding author: FAN Yu, E-mail:fanyu04@buaa.edu.cn

摘要

摘要:
含有主动材料的复合结构越来越多地应用于自适应结构中。主动纤维材料的应用为复合结构带来了新的特性也使其设计更为复杂。针对受压电纤维材料（MFC）驱动的主动材料复合板的变形进行研究，目的在于获得MFC驱动复合板扭曲变形与MFC纤维铺设及驱动模式的关系。基于弹性力学理论建立了受电压作用主动纤维产生的应变与由此导致的复合板的内力、变形之间的关系，并利用Ritz法，通过假设双向梁函数组合级数的位移场建立了该问题的求解方法，经推导得到了MFC驱动下位移场的求解方程，实验结果验证了其有效性。为了评估MFC驱动复合板在不同条件下的驱动效果，针对复合板变形所具有的弯扭耦合特点，在定义复合板截面等效扭转角和等效弯曲角的基础上提出了主动复合板驱动扭曲变形效率的概念和计算方法，利用该方法分析了MFC的铺设角度以及电压驱动模式对复合板扭曲变形效率的影响。依据分析所得到的结果给出了对应不同约束条件的MFC驱动复合板主动纤维布置及驱动模式的选择方案。
- 压电纤维材料 /
- 主动复合板 /
- 扭曲变形 /
- 纤维方向 /
- 驱动方式
Abstract:
More and more composite structures containing active materials are applied to adaptive structures. The integration of active materials in structures has brought new characteristics but made the design more complicated. In this paper, the deformation of the active composite plate actuated by the macro fiber material (MFC) is studied. The purpose is to obtain the relationship between the twist deformation of the actuated composite plate and the MFC fiber laying and the actuation mode. Based on the elastic mechanics theory, the relationship between the strain of active fiber actuated by voltage and induced internal force and deformation of the composite plate is established. The solution of the problem is conducted using Ritz's method and taking the displacement function as a linear combination of the two-dimension beam-modes. The solving equation of the displacement field actuated by MFC is derived, and the analytical result is verified by the experiment. In order to evaluate the actuation effect of MFC composite plate under different conditions and to consider the bending-torsion coupling characteristics of composite plate deformation, the concept and the calculation of actuation efficiency of an active composite plate are proposed, which is based on the definition of equivalent bending and twist angle of section. Then the evolution of the actuation efficiency with the laying angle of MFC and the mode of input voltage is analyzed. Corresponding to different constraint conditions, the laying of piezoelectric fiber-direction and the selection of actuation-mode are given based on the obtained analysis results.
- macro fiber composite /
- active composite plate /
- twist deformation /
- fiber direction /
- actuation mode

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图 1 MFC复合板的几何结构及坐标系

Figure 1. Geometry and coordinate system of MFC composite plate

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图 2 MFC复合板扭曲实验测试

Figure 2. Experimental test of twist actuation of MFC composite plate

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图 3 MFC复合板试件在MFC驱动下的位移场预测

Figure 3. Predicted displacement field of specimen (MFC composite plate) under actuation of MFC

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图 4 MFC复合板多点挠度测试与计算结果的对比

Figure 4. Comparison of deflection measurement on multi-points and calculation results of MFC composite plate

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图 5 主动材料在一体化自适应翼面中的典型应用模式

Figure 5. Typical application modes of active material in integrated adaptive wing surface

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图 6 MFC复合板等效扭转角β

Figure 6. Equivalent torsional angle β of MFC composite plate

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图 7 MFC复合板等效弯转角α

Figure 7. Equivalent bending angle α of MFC composite plate

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图 8 单层MFC驱动下压电纤维方向对复合板的自由边截面等效扭转角的影响(CFFF)

Figure 8. Effect of piezoelectric fiber direction on equivalent torsional angle at free edge section of composite plate actuated by single layer of MFC (CFFF)

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图 9 单层MFC驱动下压电纤维方向对复合板的自由边截面等效扭转角的影响(CFCF)

Figure 9. Effect of piezoelectric fiber direction on equivalent torsional angle at free edge section of composite plate actuated by single layer of MFC (CFCF)

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图 10 双层MFC复合板在(+/+)电压驱动模式下自由边截面等效扭转角、弯转角随压电纤维方向的变化(L/W=1, CFFF)

Figure 10. Evolution of equivalent torsional and bending angles at free edge section of composite plate with piezoelectric fiber direction (two layers of MFC, (+/+) actuation mode, L/W=1, CFFF)

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图 11 双层MFC复合板在(+/-)电压驱动模式下自由边截面等效扭转角、弯转角随压电纤维方向的变化(L/W=1, CFFF)

Figure 11. Evolution of equivalent torsional and bending angles at free edge section of composite plate with piezoelectric fiber direction (two layers of MFC, (+/-) actuation mode, L/W=1, CFFF)

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图 12 双层MFC复合板(+/+)电压驱动模式下压电纤维铺设角度(θ_up=-θ_down)对复合板扭曲变形效率的影响(CFFF)

Figure 12. Effect of piezoelectric fiber laying angle (θ_up=-θ_down) on efficiency of twist deformation of bimorph MFC composite plate under (+/+) actuation mode (CFFF)

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图 13 双层MFC复合板在(+/+)电压驱动模式下自由边截面等效扭转角、等效弯转角随压电纤维方向的变化(L/W=1, CFCF)

Figure 13. Evolution of equivalent torsional and bending angles at free edge section of composite plate with piezoelectric fiber direction (two layers of MFC, (+/+) actuation-mode, L/W=1, CFCF)

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图 14 双层MFC复合板在(+/-)电压驱动模式下自由边截面.等效扭转角、等效弯曲角随压电纤维方向的变化(L/W=1, CFCF)

Figure 14. Evolution of equivalent torsional and bending angles at free edge section of composite plate with piezoelectric fiber direction (two layers of MFC, (+/-) actuation-mode, L/W=1, CFCF)

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表 1 MFC和基板的材料参数

Table 1. Material parameters of MFC and substrate

材料	E/GPa		υ		G/GPa	t/mm	Λ/10^-6
材料	E₁	E₂	υ₁₂	υ₂₁	G/GPa	t/mm	Λ/10^-6
M-8528-F1	30.336	15.857	0.31	0.16	5.515	0.3	[1 350, 0, 0]^T
基底	44		0.27		3.1	0.3	—

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表 2 试件的几何参数

Table 2. Geometric parameters of specimen

试件	布置形式	x方向边界条件	y方向边界条件	W/mm	L/mm	θ_up/(°)	θ_down/(°)
1#	bimorph	C-F	F-F	35	95	45	-45

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表 3 CFFF约束的MFC复合板在2种驱动模式下的自由边截面等效扭转角极值

Table 3. Maximum equivalent torsional angles of free edge section of MFC composite plate under two actuation modes with constraint condition of CFFF

L/W	驱动模式	β_max/(°)	θ_up/(°)	θ_down/(°)
2	+/+	15.75	-46.8	46.8
2	+/-	9.50	46.8	54
1	+/+	13.90	-47.7	47.7
1	+/-	8.59	50.4	55.8
0.25	+/+	5.82	-50.4	50.4
0.25	+/-	3.93	55.8	57.6

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表 4 CFCF约束的MFC复合板在2种驱动模式下的自由边截面等效扭转角极值

Table 4. Maximum equivalent torsional angles of free edge section of MFC composite plate under two actuation modes with constraint condition of CFCF

L/W	驱动模式	β_max/(°)	θ_up/(°)	θ_down/(°)
4	+/+	3.05	-34.2	50.4
4	+/-	3.98	41.4	-34.2
1	+/+	7.84	-45	45
1	+/-	8.93	45	45
0.25	+/+	3.05	-55.8	39.6
0.25	+/-	3.98	48.6	55.8

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