基于区域分割法的正交加筋圆柱壳有限元建模及振动分析

孙雪东; 孙伟; 张荣飞; 张宏生

doi:10.13224/j.cnki.jasp.20230783

基于区域分割法的正交加筋圆柱壳有限元建模及振动分析

doi: 10.13224/j.cnki.jasp.20230783

孙雪东^{1, 2,},
孙伟^{1, 2,*, ,},
张荣飞^{1, 2},
张宏生^{1, 2}

1.
东北大学机械工程与自动化学院，沈阳 110819
2.
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

基金项目: 国家自然科学基金（12272087）

详细信息

作者简介:
孙雪东（1998-），男，硕士生，主要从事加筋薄壳动力学建模及力学性能优化研究。E-mail：927383636@qq.com

通讯作者:
孙伟（1975-），男，教授，博士，主要从事机械系统动力学及振动控制研究。E-mail：weisun@mail.neu.edu.cn

中图分类号: V231.92
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-12
- 网络出版日期: 2025-08-14

Finite element modeling and vibration analysis of the orthogonal stiffened cylindrical shell based on region segmentation method

SUN Xuedong^{1, 2
,},
SUN Wei^{1, 2,*
, ,},
ZHANG Rongfei^{1, 2},
ZHANG Hongsheng^{1, 2}

1.
School of Mechanical Engineering and Automation，Northeastern University，Shenyang 110819，China
2.
Key Laboratory of Vibration and Control of Aero-Propulsion Systems，Ministry of Education，Northeastern University，Shenyang 110819，China

摘要

摘要:
以正交加筋圆柱壳为研究对象，提出了一种基于区域分割法的有限元建模方法，旨在解决传统加强筋建模方法在非均匀加筋壳振动分析中精度不足的问题。通过将加筋壳分割为6种区域，分别推导各区域的应力-应变关系及单元刚度矩阵，并引入弹性约束边界条件，建立了正交加筋圆柱壳的动力学有限元方程。实例研究表明：在完全固定约束和螺栓弹性约束条件下，区域分割法的固有频率与ANSYS及实验结果的最大相对误差分别为3.67%和4.67%，模态置信度均高于0.90，且计算效率较涂抹加筋法提升1.3倍，较ANSYS提高了近8倍。参数分析进一步表明：蒙皮厚度对固有频率影响显著，而加强筋尺寸变化中，纵向加强筋厚度和环向加强筋宽度对固有频率的影响更为突出。
- 正交加筋圆柱壳 /
- 区域分割法 /
- 有限元法 /
- 动力学建模 /
- 振动分析
Abstract:
Taking the orthogonal stiffened cylindrical shell as the research object, a finite element modeling method based on region segmentation method was proposed to address the accuracy limitations of traditional stiffener modeling methods in analyzing vibrations of non-uniformly stiffened shells. By dividing the stiffened shell into six regions, the stress-strain relationships and element stiffness matrices for each region were derived, and elastic boundary conditions were incorporated to establish the dynamic finite element equations for the orthogonal stiffened cylindrical shell. Case studies demonstrated that under fixed and elastic constraints, the maximum relative differences of natural frequencies predicted by the region segmentation method compared with ANSYS and experimental results were 3.67% and 4.67%, respectively, with modal assurance criteria exceeding 0.90. Additionally, the computational efficiency was improved by 1.3 times over the smeared stiffener method and nearly 8 times over ANSYS. Parametric analysis further revealed that skin thickness significantly affected natural frequencies, while the thickness of longitudinal stiffeners and the width of circumferential stiffeners could play more prominent roles in influencing the natural frequencies.
- orthogonal stiffened cylindrical shell /
- region segmentation method /
- finite element method /
- dynamics modeling /
- vibration analysis

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图 1 基于区域分割法的正交加筋圆柱壳示意图

Figure 1. Schematic diagram of the orthogonal stiffened cylindrical shell based on the region segmentation method

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图 2 正交加筋圆柱壳局部放大图

Figure 2. Local amplification diagram of the orthogonal stiffened cylindrical shell

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图 3 正交加筋圆柱壳单元

Figure 3. Orthogonal stiffened cylindrical shell element

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图 4 正交加筋圆柱壳展开示意图

Figure 4. Deployment diagram of the orthogonal stiffened cylindrical shell

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图 5 周向连续均匀分布弹性约束正交加筋圆柱壳模型

Figure 5. Circumferential continuous uniform distribution elastic constraint orthogonal stiffened cylindrical shell model

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图 6 正交加筋圆柱壳模态锤击测试实验系统

Figure 6. Orthogonal stiffened cylindrical shell modal hammering test experimental system

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图 7 ANSYS固有频率及求解时间随网格数量变化

Figure 7. Natural frequencies and solution times of ANSYS vary with the number of grids

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图 8 区域分割法固有频率及求解时间随网格数量变化

Figure 8. Natural frequencies and solution times of the region segmentation method vary with the number of grid

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图 9 涂抹加筋法固有频率及求解时间随网格数量变化

Figure 9. Natural frequencies and solution times of the smeared stiffener method vary with the number of grids

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图 10 区域分割法与涂抹加筋法获得的模态振型较ANSYS的模态置信度

Figure 10. Modal assurance criterion for comparing modal shapes obtained by the region segmentation method and the smeared stiffener method with ANSYS modal shapes

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图 11 区域分割法与实验所获得的两种模态振型之间的模态置信度

Figure 11. Modal assurance criterion between the two kinds of mode shapes obtained by the region segmentation method and experiment

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图 12 蒙皮厚度变化对固有特性的影响

Figure 12. Influence of the skin thickness change on natural characteristics

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图 13 加强筋厚度变化对固有特性的影响

Figure 13. Influence of the stiffener thickness change on natural characteristics

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图 14 加强筋宽度变化对固有特性的影响

Figure 14. Influence of the stiffener width change on natural characteristics

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表 1 固支约束下正交加筋圆柱壳固有频率对比

Table 1. Comparison of natural frequencies of the orthogonal stiffened cylindrical shell under the fixed constraint

阶次	f_a/Hz	f_r/Hz	f_s/Hz	δ_r/%	δ_s/%
1	441.31	432.81	459.00	1.93	4.01
2	513.86	495.84	525.04	3.51	2.17
3	548.53	546.74	586.46	0.33	6.92
4	752.04	754.84	815.43	0.37	8.43
5	1011.90	1019.27	1105.90	0.73	9.29
6	1114.20	1087.54	1149.37	2.39	3.16
7	1133.10	1091.55	1156.12	3.67	2.03

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表 2 固支约束下正交加筋圆柱壳模态振型对比

Table 2. Comparison of modal shapes of the orthogonal stiffened cylindrical shell under the fixed constraint

阶次	ANSYS	区域分割法	涂抹加筋法
1
2
3
4
5
6
7

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表 3 弹性约束的弹簧刚度值

Table 3. Values of spring stiffness under the elastic constraint

反推辨识参数	数值
k_u /10⁴ （N/m）	1.77
k_v /10¹² （N/m）	1.17
k_w/10¹³ （N/m）	2.51
k_uθ/10¹² （N/rad）	9.66
k_vθ /10¹² （N/rad）	4.91
k_wθ/10¹² （N/rad）	3.31

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表 4 弹性约束下正交加筋圆柱壳固有频率对比

Table 4. Comparison of natural frequencies of the orthogonal stiffened cylindrical shell under the elastic constraint

阶次	f_e/Hz	f_r /Hz	δ_r/%
1	329.86	339.15	2.82
2	379.36	361.64	4.67
3	537.48	520.62	3.14
4	758.43	745.42	1.72
5	1027.20	1016.18	1.07
6	1052.78	1028.99	2.26
7	1074.79	1032.33	3.95

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表 5 弹性约束下正交加筋圆柱壳模态振型对比

Table 5. Comparison of modal shapes of the orthogonal stiffened cylindrical shell under the elastic constraint

阶次	模态实验	区域分割法
1
2
3
4
5
6
7

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