功能梯度材料圆柱杆浸入流体中的横振动

聂千钧; 李联和

doi:10.21656/1000-0887.450327

功能梯度材料圆柱杆浸入流体中的横振动

doi: 10.21656/1000-0887.450327

聂千钧^{1, 2, 3,},
李联和^{1, 2, 3, ,}

1.
内蒙古师范大学数学科学学院, 呼和浩特 010022
2.
内蒙古应用数学中心, 呼和浩特 010022
3.
无穷维哈密顿系统及其算法应用教育部重点实验室, 呼和浩特 010022

基金项目:

内蒙古自然科学基金 2023LHMS01017

内蒙古自然科学基金重点项目 2024ZD21

内蒙古自治区高校创新科研团队项目 NMGIRT2317

无穷维哈密顿系统及其算法应用教育部重点实验室开放课题 2023KFZD02

内蒙古自治区研究生科研创新基金 B20231057Z

详细信息

作者简介:
聂千钧(1998—)，男，硕士生(E-mail: 370351273@qq.com)

通讯作者:
李联和(1978—)，男，教授，博士，博士生导师(通信作者. E-mail: nmglilianhe@163.com)

中图分类号: O34
计量
- 文章访问数: 82
- HTML全文浏览量: 40
- PDF下载量: 15
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-12
- 修回日期: 2025-04-22
- 刊出日期: 2026-01-01

Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid

NIE Qianjun^{1, 2, 3
,},
LI Lianhe^{1, 2, 3
, ,}

1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China
3.
Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

摘要

摘要: 基于一阶剪切变形理论(FSDT)和势流理论，对浸没于流体中的功能梯度材料(FGM)圆柱杆进行了横振动分析. 以径向梯度指标表征金属陶瓷杆的材料性能沿径向服从幂律分布，利用分离变量法求解柱坐标系下Laplace方程，确定了流体速度势和流体动力荷载；利用Hamilton原理推导了控制方程，通过多域GDQ方法离散控制方程，结合直接迭代法计算基频与模态振型，采用CEL仿真辅助验证数值结果. 通过参数化研究，评估了长径比、梯度指标、端部边界条件以及流体深度和密度等对FGM杆-流体相互作用系统横振动行为的影响.
- 功能梯度材料 /
- 横振动 /
- Hamilton原理 /
- 广义微分正交 /
- 流固耦合
Abstract: Based on the 1st-order shear deformation theory (FSDT) and the potential flow theory, the transverse vibration of functionally graded material (FGM) cylinder bars dipped in fluid was analyzed. The cermet bar material properties following a power-law distribution along the radial direction were represented by the radial gradient index. The fluid velocity potential and hydrodynamic loads were determined through solution of the Laplace equation in cylindrical coordinates with the variable separation method. The governing equations of motion were derived according to Hamilton's principle. The fundamental frequencies and mode shapes were obtained with the generalized differential quadrature (GDQ) method and the direct iteration method. Additionally, the finite element analysis (CEL simulation) was used to validate the numerical results. Through parametric studies, the effects of the length-to-diameter ratio, the gradient index, the boundary conditions, as well as the fluid depth and density, on the transverse vibration behavior of the FGM bar-fluid interaction system were evaluated.
- FGM /
- transverse vibration /
- Hamilton's principle /
- GDQ /
- fluid-structure interaction

HTML全文

图 1 浸入流体的FGM圆柱杆的示意图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. The diagram of a FGM cylinder bar in fluid

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图 2 FGM杆横振动时自由端位移(a=1 m, n=0)

Figure 2. Displacements at the free end of the FGM bar in transverse vibration (a=1 m, n=0)

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图 3 FGM杆的密度(ρ/ρ_b)变化

Figure 3. The density (ρ/ρ_b) contour of FGM bar

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图 4 径向梯度n对FGM杆-流体相互作用系统基频的影响

Figure 4. Effects of radial gradient n on fundamental frequencies of the FGM bar-fluid interaction system

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图 5 长径比η对FGM杆-流体相互作用系统基频的影响

Figure 5. Effects of aspect ratio η on fundamental frequencies of the FGM bar-fluid interaction system

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图 6 流体密度ρ_f对FGM杆-流体相互作用系统基频的影响

Figure 6. Effects of fluid density ρ_f on fundamental frequencies of the FGM bar-fluid interaction system

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图 7 流体深度L_f对FGM杆-流体相互作用系统振动模态的影响

Figure 7. Effects of fluid depth L_f on fundamental frequencies of the FGM bar-fluid interaction system

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表 1 不同网格点数下FGM杆的基频(n=1)(单位: Hz)

Table 1. Fundamental frequencies of the FGM bar under different grid points (n=1)(unit: Hz)

N	C-C			C-F
N	L_f/L=0	L_f/L=0.5	L_f/L=1	L_f/L=0	L_f/L=0.5	L_f/L=1
5	919.3	862.9	827.9	153.2	152.1	127.5
7	942.9	886.9	819.9	155.1	154.2	137.0
9	942.1	886.7	820.2	155.1	154.2	137.2
11	942.1	886.8	820.2	155.1	154.2	137.3
13	942.1	886.9	820.2	155.1	154.2	137.4
15	942.1	886.8	820.2	155.1	154.2	137.3
17	942.1	886.9	820.2	155.1	154.2	137.4

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表 2 一端固支一端自由C-F FGM杆分别在真空和水中的基频(a=1 m, n=0)(单位: Hz)

Table 2. Fundamental frequencies of the C-F FGM bar in vacuum and in full contact with fluid (a=1 m, n=0)(unit: Hz)

boundary condition	method	L_f/L=0	L_f/L=1	ratio of frequency in water to frequency in vacuum
C-F	ref. [33]	8.21	7.48	0.911 1
	this paper	8.28	7.37	0.890 1
	CEL simulation	8.17	7.25	0.887 4

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