弹性约束边界条件下复合材料层合梁振动特性研究

赵长龙; 钟锐; 周强; 赵兴

doi:10.13433/j.cnki.1003-8728.20200091

弹性约束边界条件下复合材料层合梁振动特性研究

doi: 10.13433/j.cnki.1003-8728.20200091

赵长龙^1,,
钟锐²,
周强²,
赵兴^2, ,

1.
中车青岛四方机车车辆股份有限公司，山东青岛　266111
2.
中南大学机电工程学院，高性能复杂制造国家重点实验室，长沙　410083

基金项目: 国家重点研发计划项目（2018YFB1201901）资助

详细信息

作者简介:
赵长龙(1978−)，高级工程师，硕士，研究方向为车辆工程，zhaochanglong.sf@crrcgc.cc

通讯作者:
赵兴，讲师，xingzhao@csu.edu.cn

中图分类号: TG156
计量
- 文章访问数: 278
- HTML全文浏览量: 95
- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2019-08-13
- 刊出日期: 2020-06-05

Vibration Analysis of Laminated Composite Beams with Elastic Boundary Conditions

1.
CRCC Qingdao Sifang Co., Ltd., Shandong Qingdao 266111, China
2.
State Key Laboratory of High Performance Complex Manufacturing, College of Mechanical and Electrical Engineering , Central South University, Changsha 410083, China

摘要

摘要: 在一阶剪切变形理论和哈密顿原理的基础上，利用Haar小波离散方法，提出了一种简单、有效的评估一般弹性边界条件下复合材料层合梁振动特性的分析模型。结构位移变量及其相关导数的基函数分别采用Haar小波及其积分表示。在此基础上，利用边界条件求出积分过程中的常数，进而将层合梁的运动方程和边界条件进一步转化为一组线性代数方程。通过求解该线性代数方程，可得到复合材料层合梁的自由振动特性。通过数值算例对比验证了本文模型的正确性。此外，给出了复合材料层合梁的一些新的计算结果，可作为基准解为后续数值方法或解析法提供对比数据。
- Haar小波 /
- 复合材料层合梁 /
- 一阶剪切变形理论 /
- 自由振动
Abstract: A simple and efficient method is proposed to evaluate the vibration behavior of the laminated composite beams under elastic boundary conditions with Haar wavelet discretization method, in terms of the first order shear deformation theory and the Hamilton principle. The basis functions for the displacement variables and their derivatives are expressed in terms of Haar wavelet and their integral, respectively. On the basis, the boundary conditions are used to obtain the constants in the integration process, and then the equations of motion and the boundary conditions of the laminated beams are further converted into a group of linear algebraic equations. The natural frequencies of laminated composite beams are obtained by solving the algebraic equations. The correctness and efficiency of the present method is verified by a series of numerical examples. Some new results for the laminated composite beams are presented, which may serve as benchmark solutions.
- Haar wavelet discretization method /
- laminated composite beams /
- first order shear deformation /
- free vibration

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图 1 复合材料层合梁几何模型

下载: 全尺寸图片幻灯片

图 2 不同最大尺度因子J下两端固支复合材料层合梁的频率参数Ω

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图 3 不同边界参数下复合材料层合梁的频率参数Ω

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表 1 不同边界条件下对应的弹簧刚度值

弹簧类型	经典边界条件			弹性边界条件
弹簧类型	F	S	C	E₁	E₂	E₃
${k_u}_{,0},\;{k_u}_{,L}$	0	10¹⁴	10¹⁴	10⁸	10¹⁴	10⁸
${k_{w,}}_0,\;{k_{w,}}_L$	0	10¹⁴	10¹⁴	10⁸	10¹⁴	10⁸
${k_{\varphi ,0}},\;{k_{\varphi ,L}}$	0	0	10¹⁴	10¹⁴	10⁸	10⁸

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表 2 不同边界条件下复合材料层合梁固有频率对比

边界条件	模态阶次	本文方法	文献 [12]	文献 [13]	文献 [14]
	1	639.08	638.50	637.20	637.90
	2	1 656.3	1 657.3	1 653.2	1 647.8
C-C	3	3 026.6	3 034.0	3 025.0	3 000.0
	4	4 640.2	4 661.2	4 644.8	3 911.0
	5	4 950.6	4 784.6	4 960.8	4 587.3
	1	105.49	105.30	105.10	105.30
	2	638.40	637.60	636.40	635.00
C-F	3	1 698.9	1 698.0	1 694.2	1 678.9
	4	2 475.5	2 392.3	2 480.6	1 970.6
	5	3 119.7	3 121.0	3 113.2	2 546.2
	1	660.42	659.30	659.20	655.00
	2	1 741.8	1 738.6	1 735.2	1 719.2
F-F	3	3 219.5	3 213.4	3 207.2	3 128.8
	4	4 951.2	4 784.8	4 948.0	3 966.8
	5	4 969.8	4 961.0	4 961.6	4 836.5
	1	295.33	294.80	294.90	353.70
	2	1 134.5	1 132.4	1 130.2	1 114.3
S-S	3	2 418.9	2 414.4	2 490.6	2 434.2
	4	4 021.2	4 012.3	4 001.1	3 450.3
	5	4 949.3	4 784.2	4 952.9	4 264.5
	1	451.09	450.50	449.80	467.30
	2	1 390.9	1 389.9	1 387.0	1 391.3
S-C	3	2 723.9	2 724.1	2 717.5	2 685.5
	4	4 336.0	4 340.4	4 327.8	3 757.0
	5	4 949.6	4 784.3	4 956.1	4 366.8

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表 3 不同边界条件下复合材料层合梁固有频率对比

模态阶次	边界条件
	C-C			C-F		S-C		S-S
	本文方法	文献[12]	文献[14]	本文方法	文献[12]	本文方法	文献[12]	本文方法	文献[12]
1	1 054.598	1 054.503	1 054.4	191.85	191.80	785.07	784.90	559.04	558.90
2	2 509.615	2 509.363	2 509.2	1 088.6	1 088.5	2 224.2	2 223.9	1 908.0	1 907.7
3	4 282.239	4 281.739	4 281.5	2 694.2	1 132.7	4 039.2	4 038.6	3 787.8	3 787.2
4	6 216.956	6 216.093	6 215.8	4 598.9	2 265.4	6 032.6	6 301.5	5 826.0	5 824.8
5	8 241.754	8 240.392	8 239.9	4 905.2	2 693.8	8 106.6	8 104.8	7 982.3	7 980.5

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参考文献(15)

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