面内功能梯度三角形板等几何面内振动分析

陈明飞; 刘坤鹏; 靳国永; 张艳涛; 叶天贵; 刘志刚

doi:10.21656/1000-0887.400171

面内功能梯度三角形板等几何面内振动分析

doi: 10.21656/1000-0887.400171

哈尔滨工程大学动力与能源工程学院, 哈尔滨 150001

基金项目: 国家自然科学基金（51775125;51822902;51709066）;中央高校基本科研基金（HEUCF180305）

详细信息

作者简介:
陈明飞（1990—），男，黎族，博士生(E-mail: mingfeichen@hrbeu.edu.cn);叶天贵（1989—），男，副教授(通讯作者. E-mail: yetiangui@gmail.com).

中图分类号: O326
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- 文章访问数: 1759
- HTML全文浏览量: 360
- PDF下载量: 406
- 被引次数: 0
出版历程
- 收稿日期: 2019-05-15
- 修回日期: 2019-12-25
- 刊出日期: 2020-02-01

Isogeometric in-Plane Vibration Analysis of Functionally Graded Triangular Plates

College of Power and Energy Engineering, Harbin Engineering University,Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China（51775125;51822902;51709066）

摘要

摘要: 基于平面应变理论，利用等几何有限元方法分析了弹性边界条件下面内功能梯度三角形板的面内振动特性。板的材料属性沿厚度方向呈均匀分布，而在面内方向呈任意指数梯度变化。采用非均匀有理B样条（NURBS）基函数对三角形结构进行等几何建模和位移描述，实现了三角形板几何设计和振动分析的无缝衔接。在三角形板边界上引入虚拟弹簧约束并通过调节虚拟弹簧刚度，实现任意边界条件的施加。通过不同的单元细化方案和对比算例，验证了等几何方法的灵活性、准确性和快速收敛性。系统研究了边界条件、材料属性和几何参数对三角形板振动特性的影响。同时给出了弹性边界条件下面内功能梯度三角形板的振动特性解，具有重要参考价值.
- 三角形板 /
- 等几何分析 /
- NURBS /
- 面内振动 /
- 功能梯度材料 /
- 有限元
Abstract: The in-plane vibration of the triangular plates of in-plane functionally graded (IFG) materials based on the plane stress theory was investigated by means of isogeometric analysis (IGA). The material of the triangular plate is homogenous in the thickness direction, but functionally graded along the in-plane direction. The geometry and displacement field of the considered plate were constructed with the non-uniform rational B-splines (NURBS) basis functions, then a seamless integration of the geometric design and the vibration characteristic analysis of the triangular plate was realized. The arbitrary boundary conditions of the triangular plate were obtained through adjustment of the stiffness of artificial springs introduced into the boundary of the triangular plate. The flexibility, high accuracy and quick convergency of the proposed method were verified through different refinements and results comparison. Finally, effects of boundary conditions, material properties and geometry parameters were investigated systematically. The vibration solutions of many kinds of triangular plates of in-plane functionally graded materials with elastic boundary conditions were given. The work provides a good reference for engineering application.
- triangular plate /
- isogeometric analysis /
- NURBS /
- in-plane vibration /
- functionally graded material /
- finite element method

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参考文献(26)

[1]	MIYAMOTO Y, KAYSSER W A, RABIN B H, et al. Functionally Graded Materials: Design, Processing and Applications [M]. Berlin: Springer, 1999.
[2]	DELFOSSE D. Fundamentals of functionally graded materials[J]. Materials Today,1998,1(4): 18.
[3]	TALHA M, SINGH B N. Large amplitude free flexural vibration analysis of shear deformable FGM plates using nonlinear finite element method[J]. Finite Elements in Analysis & Design,2011,47(4): 394-401.
[4]	叶天贵, 靳国永, 刘志刚. 多层复合壳体三维振动分析的谱-微分求积混合法[J]. 力学学报, 2018,50(4): 847-852.(YE Tiangui, JIN Guoyong, LIU Zhigang. A spectral-differential quadrature method for 3-D vibration analysis of multilayered shells[J]. Chinese Journal of Theoretical and Applied Mechanics,2018,50(4): 847-852.(in Chinese))
[5]	SU Z, JIN G, YE T. Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints[J]. Composite Structures,2014,118: 432-447.
[6]	ZHANG C, JIN G, YE T, et al. Harmonic response analysis of coupled plate structures using the dynamic stiffness method[J]. Thin-Walled Structures,2018,127: 402-415.
[7]	SU Z, JIN G, YE T. Free vibration analysis of moderately thick functionally graded open shells with general boundary conditions[J]. Composite Structures,2014,117: 169-186.
[8]	EBRAHIMI F, RASTGO A. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory[J]. Thin-Walled Structures,2008,46(12): 1402-1408.
[9]	XUE Y, JIN G, DING H, et al. Free vibration analysis of in-plane functionally graded plates using a refined plate theory and isogeometric approach[J]. Composite Structures,2018,192: 193-205.
[10]	YIN S, YU T, BUI T Q, et al. In-plane material inhomogeneity of functionally graded plates: a higher-order shear deformation plate isogeometric analysis[J]. Composites Part B: Engineering,2016,106: 273-284.
[11]	倪振华. 振动力学[M]. 西安: 西安交通大学, 1989.(NI Zhenghua. Mechanics of Vibration [M]. Xi’an: Xi’an Jiaotong University Press, 1989.(in Chinese))
[12]	黄炎, 雷勇军, 申慧君. 各向异性矩形板自由振动的一般解析解法[J]. 应用数学和力学, 2006,27(4): 411-416.(HUANG Yan, LEI Yongjun, SHEN Huijun. Free vibration of anisotropic rectangular plates by general analytical method[J]. Applied Mathematics and Mechanics,2006,27(4): 411-416.(in Chinese))
[13]	瞿叶高, 华宏星, 谌勇, 等. 复合材料旋转壳自由振动分析的新方法[J]. 力学学报, 2013,45(1): 139-143 (QU Yegao, HUA Hongxing, CHEN Yong, et al. A new method for free vibration analysis of composite laminated shells of revolution[J]. Chinese Journal of Theoretical and Applied Mechanic s, 2013,45(1): 139-143.(in Chinese))
[14]	QIN Z, CHU F, ZU J. Free vibrations of cylindrical shells with arbitrary boundary conditions: a comparison study[J]. International Journal of Mechanical Sciences,2017,133: 91-99.
[15]	王云, 徐荣桥, 丁皓江. 功能梯度圆板的轴对称自由振动[J]. 应用数学和力学, 2009,30(9): 1009-1014.(WANG Yun, XU Rongjiao, DING Haojiang. Free axisymmetric vibration of FGM circular plates[J]. Applied Mathematics and Mechanics,2009,30(9): 1009-1014.(in Chinese))
[16]	曹志远, 唐寿高, 程国华. 复杂形状及开孔功能梯度板的三维分析[J]. 应用数学和力学, 2009,30(1): 15-20.(CAO Zhiyuan, TANG Shougao, CHENG Guohua. 3D analysis of the functionally graded material plates with complex shapes and various holes[J]. Applied Mathematics and Mechanics,2009,30(1): 15-20.(in Chinese))
[17]	LIU D Y, WANG C Y, CHEN W Q. Free vibration of FGM plates with in-plane material inhomogeneity[J]. Composite Structures,2010,92(5): 1047-1051.
[18]	MALEKZADEH P, BENI A A. Nonlinear free vibration of in-plane functionally graded rectangular plates[J]. Mechanics of Composite Materials & Structures,2015,22(8): 633-640.
[19]	HUGHES T J R, COTTRELL J A, BAZILEVS Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(39/41): 4135-4195.
[20]	YU T, YIN S, TINH Q B, et al. A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates[J]. Finite Elements in Analysis Design,2015,96: 1-10.
[21]	YIN S, HALE J S, YU T, et al. Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates[J]. Composite Structures,2014,118(1): 121-38.
[22]	CHEN M, JIN G, ZHANG Y, et al. Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thickness[J]. Composite Structures,2019,207: 304-322.
[23]	CHEN M, JIN G, MA X, et al. Vibration analysis for sector cylindrical shells with bi-directional functionally graded materials and elastically restrained edges[J]. Composites Part B: Engineering,2018,153: 346-363.
[24]	CHEN M, CHEN H, MA X, et al. The isogeometric free vibration and transient response of functionally graded piezoelectric curved beam with elastic restraints[J]. Results in Physics,2018,11: 712-725.
[25]	PIEGL L, TILLER W. The Nurbs Books [M]. 2nd ed. Berlin: Springer-Verlag, 1995.
[26]	CHEN M, JIN G, YE T, et al. An isogeometric finite element method for the in-plane vibration analysis of orthotropic quadrilateral plates with general boundary restraints[J]. International Journal of Mechanical Sciences,2017,133: 846-862.

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面内功能梯度三角形板等几何面内振动分析

doi: 10.21656/1000-0887.400171

作者简介:
陈明飞（1990—），男，黎族，博士生(E-mail: mingfeichen@hrbeu.edu.cn);叶天贵（1989—），男，副教授(通讯作者. E-mail: yetiangui@gmail.com).

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Isogeometric in-Plane Vibration Analysis of Functionally Graded Triangular Plates

计量

目录

留言板

面内功能梯度三角形板等几何面内振动分析

doi: 10.21656/1000-0887.400171

作者简介: 陈明飞（1990—），男，黎族，博士生(E-mail: mingfeichen@hrbeu.edu.cn);叶天贵（1989—），男，副教授(通讯作者. E-mail: yetiangui@gmail.com).

计量

出版历程

Isogeometric in-Plane Vibration Analysis of Functionally Graded Triangular Plates

计量

出版历程

目录

作者简介:
陈明飞（1990—），男，黎族，博士生(E-mail: mingfeichen@hrbeu.edu.cn);叶天贵（1989—），男，副教授(通讯作者. E-mail: yetiangui@gmail.com).