基于Galerkin法研究应力波作用下复合材料板的动力学失稳

王志鹏; 韩志军; 王龙飞

doi:10.11858/gywlxb.20210705

基于Galerkin法研究应力波作用下复合材料板的动力学失稳

doi: 10.11858/gywlxb.20210705

王志鹏^1,,
韩志军^2,*, ,,
王龙飞²

1.
太原理工大学机械与运载工程学院，山西太原　030024
2.
太原理工大学生物医学工程学院，山西太原　030024

基金项目: 国家自然科学基金（11802195）

详细信息

作者简介:
王志鹏（1994－），男，硕士，主要从事非线性动力屈曲研究. E-mail：694596123@qq.com

通讯作者:
韩志军（1964－），男，博士，教授，主要从事非线性动力屈曲研究. E-mail：13073578705@126.com

中图分类号: O343.5
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出版历程
- 收稿日期: 2021-01-10
- 修回日期: 2021-02-05

Dynamic Instability of Composite Plate under Stress Wave Based on Galerkin Method

1.
College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 基于Kirchhoff薄板理论和Hamilton原理，考虑应力波效应，对含初始几何缺陷的三边简支、一边固支的复合材料板，建立了振动控制方程，得到了其屈曲临界荷载表达式。采用MATLAB编程进行数值计算，讨论了初始几何缺陷、初相位、铺层角度、屈曲模态阶数及铺层层数对板屈曲临界荷载的影响。结果表明：复合材料板的屈曲临界载荷随临界长度增大、铺设厚度减小、初始几何缺陷系数增大、振型函数初相位减小而减小。此外，复合材料板的各层铺层角度与荷载作用方向的夹角越小，屈曲临界载荷越大，当板的对称铺设层数达到7层时，临界荷载趋于稳定。
- 复合材料板 /
- 应力波效应 /
- 初始几何缺陷 /
- 屈曲 /
- 临界荷载
Abstract: Based on the Kirchhoff thin plate theory and Hamilton principle, the vibration control equation of composite plate is established. The equation is simply supported on three sides and fixed on one side with initial geometric imperfections. The expression of buckling critical load is obtained. The numerical calculation is carried out by MATLAB programming. The effects of initial geometric imperfections, initial phase, ply angle, buckling mode order and layer number on the critical buckling load of the plate are discussed. Results show that the critical buckling load is decrease with the increasing of the critical length, the decreasing of the laying thickness, the increasing of the initial geometric defect coefficient, and the decreasing of the initial phase of the mode function. In addition, the smaller the angle between the laying angle of each layer and the load direction is, the greater the buckling critical load is. And the buckling critical load tends to be stable when the layer number of symmetrical laminate reaches seven.
- composite plate /
- effect of stress wave /
- initial geometric defect /
- buckling /
- critical load

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图 1 复合材料板结构示意图

Figure 1. Schematic diagram of composite plate structure

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图 2 应力波传播示意图

Figure 2. Schematic diagram of stress wave propagation

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图 3 x方向模态取值增大时板的屈曲模态

Figure 3. Buckling mode of composite plate with increasing mode value in x direction

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图 4 不同初始缺陷系数条件下N_cr与L_cr的关系曲线

Figure 4. Relationship between N_cr and L_cr under different initial defect coefficients

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图 5 x方向模态阶数不同时N_cr与L_cr的关系曲线

Figure 5. Relationship between N_cr and L_cr with different order of modes in x direction

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图 6 y方向模态阶数不同时N_cr与L_cr的关系曲线

Figure 6. Relationship between N_cr and L_cr with different order of modes in y direction

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图 7 不同铺层角度条件下N_cr与L_cr的关系曲线

Figure 7. Relationship between N_cr and L_cr under different laying angles

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图 8 不同初相位条件下N_cr与L_cr的关系曲线

Figure 8. Relationship between N_cr and L_cr under the condition of initial phase of different mode functions

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图 9 不同铺层层数下N_cr与L_cr的关系曲线

Figure 9. Relationship between N_cr and L_cr under different laying modes

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图 10 不同铺设厚度下N_cr与L_cr的关系曲线

Figure 10. Relationship between N_cr and L_cr under different thicknesses

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表 1 复合材料板参数^[21]

Table 1. Material parameters of composite plate^[21]

E₁/GPa	E₂/GPa	G₁₂/GPa	μ₁₂	L_a/m	L_b/m
140.0	8.6	5.0	0.35	0.60	0.50

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表 2 算例分析参数表

Table 2. Example analysis parameter table

Group	Initial defect coefficient	Order of mode		Laying angle/(°)	Initial phase	Number of layers laid	Thickness of the plate/m
Group	Initial defect coefficient	x direction	y direction	Laying angle/(°)	Initial phase	Number of layers laid	Thickness of the plate/m
A	Variable	i = 1	j = 1	[0, 0, 0, 0, 0]	$ {\text{π}}$/2	5	0.01
B	0.1	Variable	j = 1	[0, 0, 0, 0, 0]	$ {\text{π}}$/2	5	0.01
C	0.1	i =1	Variable	[0, 0, 0, 0, 0]	$ {\text{π}}$/2	5	0.01
D	0.1	i =1	j = 1	Variable	$ {\text{π}}$/2	5	0.01
E	0.1	i =1	j = 1	[0, 0, 0, 0, 0]	Variable	5	0.01
F	0.1	i =1	j = 1	[0, 0, 0, 0, 0]	$ {\text{π}}$/2	Variable	0.01
G	0.1	i =1	j = 1	[0, 0, 0, 0, 0]	$ {\text{π}}$/2	5	Variable

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