纤维增强截顶圆锥壳固有特性计算及分析

许卓; 许沛尧; 郑利胜; 李晖; 李鹤; 顾大卫; 何明阳; 韩清凯; 闻邦椿

doi:10.13224/j.cnki.jasp.20220876

纤维增强截顶圆锥壳固有特性计算及分析

doi: 10.13224/j.cnki.jasp.20220876

许卓^{1, 3,},
许沛尧¹,
郑利胜²,
李晖^{3, 4,*, ,},
李鹤^{3, 4},
顾大卫^{4, 5},
何明阳¹,
韩清凯^{3, 4},
闻邦椿^{3, 4}

1.
东北电力大学机械工程学院，吉林 132011
2.
温州市工业科学研究院，浙江温州 325028
3.
东北大学机械工程与自动化学院，沈阳 110819
4.
东北大学航空动力装备振动及控制教育部重点实验室，沈阳 110819
5.
浙江工业大学机械工程学院，杭州 310014

基金项目: 东北电力大学博士科研启动基金（BSJXM-2020221）；东北大学航空动力装备振动及控制教育部重点实验室研究基金（VCAME202204）

详细信息

作者简介:
许卓（1986-），男，讲师，博士，主要从事复合结构减振降噪研究。E-mail：zhuoluo0816@163.com

通讯作者:
李晖（1982−），男，副教授，博士，主要从事复合结构减振降噪研究。E-mail：lh200300206@163.com

中图分类号: V214.3⁺3
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- 被引次数: 0
出版历程
- 收稿日期: 2022-11-16
- 网络出版日期: 2024-04-10

Natural characteristics calculation and analysis of fiber reinforced truncated conical shell

XU Zhuo^{1, 3
,},
XU Peiyao¹,
ZHENG Lisheng²,
LI Hui^{3, 4,*
, ,},
LI He^{3, 4},
GU Dawei^{4, 5},
HE Mingyang¹,
HAN Qingkai^{3, 4},
WEN Bangchun^{3, 4}

1.
School of Mechanical Engineering，Northeast Electric Power University，Jilin 132011，China
2.
Wenzhou Institute of Industry and Science，Wenzhou Zhejiang 325028，China
3.
School of Mechanical Engineering and Automation，Northeastern University，Shenyang 110819，China
4.
Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education，Northeastern University，Shenyang 110819，China
5.
School of Mechanical Engineering，Zhejiang University of Technology，Hangzhou 310014，China

摘要

摘要:
以理论与实践相结合的方式分析了纤维增强截顶圆锥壳的固有特性。针对纤维增强复合圆锥壳的结构特性引入半锥角系数，考虑复合结构各向异性的影响，基于经典层合理论对其进行了理论建模；利用Rayleigh-Ritz法和正交多项式法求解了结构的固有特性。通过搭建相应的实验系统，以TC300/环氧树脂复合圆锥壳为研究对象进行测试，结果表明：该方法所获得固有频率的结果与试验测试结果间的误差在1.4%～2.3%之间，进而验证了所提出模型的正确性。最后，讨论了半锥角大小、不同约束方式和不同纤维铺层角度等参数对结构固有特性的影响规律。
- 纤维增强复合结构 /
- 截顶圆锥壳 /
- 固有特性 /
- Rayleigh-Ritz法 /
- 正交多项式
Abstract:
The natural characteristics of composite conical shells were calculated and verified by combining theory and experiment. Based on the classical lamination theory and considering the influence of anisotropy of composite structures, the theoretical model was established by introducing half-cone angle coefficients. Then, the natural characteristics of the structures were obtained by utilizing the Rayleigh-Ritz method and orthogonal polynomial method. A natural characteristic experiment system of TC300/epoxy resin composite conical shell was established and the natural characteristics were acquired. The results showed that the error between the calculated and test results was between 1.4% and 2.3%, which further verified the correctness of the proposed model. Finally, the influences of different parameters, such as the half cone angle, the boundary conditions and the fiber ply angles, on the natural characteristics of the structure were discussed.
- fiber reinforced composite structures /
- truncated conical shell /
- natural characteristics /
- Rayleigh-Ritz /
- orthogonal polynomial

HTML

图 1 纤维增强截顶圆锥壳理论模型

Figure 1. Theoretical model of fiber reinforced truncated conical shell

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图 2 薄壳的固有特性测试系统

Figure 2. Test system for inherent properties of thin shells

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图 3 频率-振幅关系曲线

Figure 3. Frequency-amplitude curve

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图 4 半锥角演化示意图

Figure 4. Schematic diagram of semi-conical angle evolution

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图 5 纤维增强截顶圆锥壳不同固定端示意图

Figure 5. Schematic diagram of fiber reinforced truncated conical shell under different constraint boundary conditions

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图 6 纤维增强截顶圆锥壳不同铺层角度示意图

Figure 6. Schematic diagram of fiber reinforced truncated conical shell with different laid methods

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表 1 计算和测试获得的纤维增强截顶圆锥壳的前3阶固有频率和模态振型

Table 1. Calculation and testing of the first seventh-order intrinsic frequencies and modal shapes of thin fiber-metal composite shells obtained

参数		模态阶次
参数		1	2	3
频率/Hz	实验频率A	716.22	1 217.30	1 670.10
	Matlab计算频率B	705.23	1 246.16	1 645.50
	Ansys计算频率C	726.28	1 157.70	1 756.90
误差/%	\|A−B\|/B	1.5	2.3	1.4
	\|A−C\|/C	1.3	5.1	4.9
	\|B−C\|/B	2.9	7.1	6.7
振型图	Matlab
振型图	Ansys

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表 2 不同半锥角下的纤维增强截顶圆锥壳固有频率

Table 2. Natural frequencies of fiber reinforced truncated conical shell with different semi-conical angle

α/（°）	频率相关参数		模态阶次
α/（°）	频率相关参数		1	2	3	4	5	6
0	频率/Hz	A₁（Matlab）	977.92	1 637.82	1 953.57	2 284.71	2 796.62	3 166.14
	频率/Hz	B₁（Ansys）	923.48	1 583.40	1 884.50	2 312.70	2 845.30	3 094.80
	误差/%	\|A₁−B₁\|/A₁	5.5	3.3	3.5	1.2	1.7	2.3
30	频率/Hz	A₂（Matlab）	705.23	1 246.16	1 645.50	1 934.49	2 450.27	2 864.31
	频率/Hz	B₂（Ansys）	726.28	1 157.70	1 756.90	1 987.60	2 412.20	2 764.30
	误差/%	\|A₂−B₂\|/A₂	2.9	7.1	6.7	2.7	1.6	3.5
60	频率/Hz	A₃（Matlab）	436.22	954.84	1 361.34	1 799.95	2 116.60	2 54869
	频率/Hz	B₃（Ansys）	414.51	1 002.70	1 271.30	1 844.80	2 199.10	2 516.10
	误差/%	\|A₃−B₃\|/A₃	5.0	5.0	6.6	2.5	3.9	1.3
90	频率/Hz	A₄（Matlab）	143.65	642.99	1 049.54	1 381.93	1 867.34	2 212.62
	频率/Hz	B₄（Ansys）	138.94	611.34	992.77	1 422.30	1 912.60	2 185.70
	误差/%	\|A₄−B₄\|/A₄	3.3	4.9	5.4	3.1	2.4	1.2

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表 3 不同固定端下纤维增强截顶圆锥壳的固有频率

Table 3. Natural frequencies of fiber reinforced truncated conical shell under different boundary conditions

固定方式	频率相关参数		模态阶次
固定方式	频率相关参数		1	2	3	4	5	6
小端固定	频率/Hz	A₁（Matlab）	366.42	595.88	994.26	1 290.31	1 455.60	1 831.46
	频率/Hz	B₁（Ansys）	348.33	618.74	1 022.20	1 272.10	1 489.60	1 795.50
	误差/%	\|A₁−B₁\|/A₁	4.9	3.8	2.8	1.4	2.3	1.9
大端固定	频率/Hz	A₂（Matlab）	705.23	1 246.16	1 645.50	1 934.49	2 450.27	2 864.31
	频率/Hz	B₂（Ansys）	726.28	1 157.70	1 756.90	1 987.60	2 412.20	2 764.30
	误差/%	\|A₂−B₂\|/A₂	2.9	7.1	6.7	2.7	1.6	3.5
两端固定	频率/Hz	A₃（Matlab）	1 012.72	1 368.45	1 746.77	2 106.82	2 341.16	2 623.42
	频率/Hz	B₃（Ansys）	998.54	1 390.50	1 774.50	2 081.90	2 323.70	2 658.50
	误差/%	\|A₃−B₃\|/A₃	1.4	1.6	1.6	1.2	0.7	1.3
两端自由	频率/Hz	A₄（Matlab）	124.16	216.34	314.59	475.38	598.73	715.64
	频率/Hz	B₄（Ansys）	116.27	208.01	298.75	441.21	618.40	740.44
	误差/%	\|A₄−B₄\|/A₄	6.3	3.8	5.0	7.1	3.2	3.4

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表 4 不同铺层角度下纤维增强截顶圆锥壳的固有频率

Table 4. Natural frequencies of fiber reinforced truncated conical shell with different laid methods

铺层角度	频率相关参数		模态阶次
铺层角度	频率相关参数		1	2	3	4	5	6
[0°/90°]_s	频率/Hz	A₁（Matlab）	441.94	987.35	1 435.64	1 895.46	2 334.71	2 791.86
	频率/Hz	B₁（Ansys）	422.57	1 002.42	1 519.20	1 822.80	2 284.70	2 680.20
	误差/%	\|A₁−B₁\|/A₁	4.3	1.5	5.5	3.8	2.1	3.9
[+45°/−45°]_s	频率/Hz	A₂（Matlab）	705.23	1 246.16	1 645.50	1 934.49	2 450.27	2 864.31
	频率/Hz	B₂（Ansys）	726.28	1 157.70	1 756.90	1 987.60	2 412.20	2 764.30
	误差/%	\|A₂−B₂\|/A₂	2.9	7.1	6.7	2.7	1.6	3.5
[90°/90°]_s	频率/Hz	A₃（Matlab）	912.34	1 132.60	1 455.74	1 725.34	2 236.68	2 886.43
	频率/Hz	B₃（Ansys）	955.34	1 160.50	1 500.10	1 795.30	2 331.00	1 986.40
	误差/%	\|A₃−B₃\|/A₃	4.7	2.4	3.0	4.0	4.2	3.1

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