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论文:2021,Vol:39,Issue(2):317-325 |
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引用本文： |
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滕兆春, 席鹏飞. 多孔FGM矩形板的自由振动与临界屈曲载荷分析[J]. 西北工业大学学报 |
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TENG Zhaochun, XI Pengfei. Analysis on free vibration and critical buckling load of a FGM porous rectangular plate[J]. Northwestern polytechnical university |
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| 多孔FGM矩形板的自由振动与临界屈曲载荷分析 |
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| 滕兆春, 席鹏飞 |
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| 兰州理工大学 理学院, 甘肃 兰州 730050 |
| 摘要: |
| 功能梯度材料（FGM）的特性与孔隙量有密切的关系，孔隙率会影响FGM的弹性模量、泊松比和密度等。依据经典薄板理论和Hamilton原理建立了四边受压多孔FGM矩形板自由振动和屈曲的数学模型并对控制方程进行无量纲化。运用微分变换法（DTM）对无量纲控制微分方程及其边界条件进行变换，经过迭代求解，得到多孔FGM矩形板的无量纲固有频率和无量纲临界屈曲载荷。将该问题退化为孔隙率为零时FGM矩形板的自由振动并与其精确解进行对比，发现DTM计算精度较高，这验证了该方法在求解四边受压多孔FGM矩形板自由振动和屈曲问题的有效性。计算结果表明，多孔FGM矩形板的弹性模量随梯度指数与孔隙率的增大而减小。进一步分析了在不同边界条件下长宽比不变时梯度指数、孔隙率对无量纲的固有频率和临界屈曲载荷的影响，以及不同边界条件下长宽比、载荷对无量纲固有频率的影响。 |
| 关键词:
多孔FGM
矩形板
孔隙率
自由振动
屈曲
微分变换法
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| Analysis on free vibration and critical buckling load of a FGM porous rectangular plate |
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| TENG Zhaochun, XI Pengfei |
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| School of Science, Lanzhou University of Technology, Lanzhou 730050, China |
| Abstract: |
| The properties of functionally gradient materials (FGM) are closely related to porosity, which has effect on FGM's elastic modulus, Poisson's ratio, density, etc. Based on the classical theory of thin plates and Hamilton principle, the mathematical model of free vibration and buckling of FGM porous rectangular plates with compression on four sides is established. Then the dimensionless form of the governing differential equation is also obtained. The dimensionless governing differential equation and its boundary conditions are transformed by differential transformation method (DTM). After iterative convergence, the dimensionless natural frequencies and critical buckling loads of the FGM porous rectangular plate are obtained. The problem is reduced to the free vibration of FGM rectangular plate with zero porosity and compared with its exact solution. It is found that DTM gives high accuracy result. The validity of the method is verified in solving the free vibration and buckling problems of the porous FGM rectangular plates with compression on four sides. The results show that the elastic modulus of FGM porous rectangular plate decreases with the increase of gradient index and porosity. Furthermore, the effects of gradient index and porosity on dimensionless natural frequencies and critical buckling loads are further analyzed under different boundary conditions with constant aspect ratio, and the effects of aspect ratio and load on dimensionless natural frequencies under different boundary conditions. |
| Key words:
porous FGM
rectangular plate
porosity
free vibration
buckling
differential transformation method (DTM)
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| 收稿日期: 2020-06-29
修回日期:
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| DOI: 10.1051/jnwpu/20213920317 |
| 基金项目: 国家自然科学基金（11662008）资助 |
| 通讯作者:
Email： |
| 作者简介: 滕兆春(1969-),兰州理工大学副教授、硕士生导师,主要从事智能材料与结构力学、结构动力学研究。
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参考文献: |
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[1] 马涛,赵忠民,刘良祥,等. 功能梯度材料的研究进展及应用前景[J]. 化工科技,2012,20(1):71-75 MA Tao, ZHAO Zhongmin, LIU Liangxiang, et al. The research development and future application of functionally gradient materials[J]. Science & Technology in Chemical Industry, 2012, 20(1):71-75(in Chinese)
[2] REN X, FAN H, WANG C, et al. Coaxial rotatory-freestanding triboelectric nanogenerator for effective energy scavenging from wind[J]. Smart Materials and Structures, 2018, 27(6):065016
[3] ZENG X, FAN H, ZHANG J. Prediction of the effects of particle and matrix morphologies on Al2O3 particle/polymer composites by finite element method[J]. Computational Materials Science, 2007, 40(3):395-399
[4] WANG B, ZHU D, LI C, et al. Performance of full compositional W/Cu functionally gradient materials under quasi-steady-state heat loads[J]. IEEE Trans on Plasma Science, 2018, 46(5):1551-1555
[5] SHISHESAZ M, HOSSEINI M, NADERAN TAHAN K, et al. Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory[J]. Acta Mechanica, 2017, 228(12):4141-4168
[6] STATHOPOULOS V, SADYKOV V, PAVLOVA S, et al. Design of functionally fraded multilayer thermal barrier coatings for gas turbine application[J]. Surface and Coatings Technology, 2016, 295:20-28
[7] WAN Y P, SAMPATH S, PRASAD V, et al. An advanced model for plasma spraying of functionally graded materials[J]. Journal of Materials Processing Technology, 2003, 137(1/2/3):110-116
[8] SHCHUKIN A S, VREL D, SYTSCHEV A E. Interaction of NiAl intermetallic during SHS synthesis with Ta substrate[J]. Advanced Engineering Materials, 2018, 20(8):1701077
[9] 黄旭涛, 严密. 功能梯度材料:回顾与展望[J]. 材料科学与工程, 1997, 15(4):35-38 HUANG Xutao, YAN Mi. Review and prospects of functionally gradient materials[J]. Materials Science and Engineering, 1997, 15(4):35-38(in Chinese)
[10] SPRIGGS R M. Expression for effect of porosity on elastic modulus of polycrystalline refractory materials, particularly aluminum oxide[J]. Journal of the American Ceramic Society, 1961, 44(12):628-629
[11] POHANKA R C, RICE R W, WALKER B E. Effect of internal stress on the strength of BaTiO3[J]. Journal of the American Ceramic Society, 1976, 59(1/2):71-74
[12] WANG J C. Young's modulus of porous materials[J]. Journal of Materials Science, 1984, 19(3):809-814
[13] PHANI K K, NIYOGI S K. Young's modulus of porous brittle solids[J]. Journal of Materials Science, 1987, 22(1):257-263
[14] RAMAKRISHNAN N, ARUNACHALAM V S. Effective elastic moduli of porous solids[J]. Journal of Materials Science, 1990, 25(9):3930-3937
[15] KIRAN M C, KATTIMANI S. Assessment of porosity influence on vibration and static behaviour of functionally graded magneto-electro-elastic plate:a finite element study[J]. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2020, 1(44):61-82
[16] BEHRAVAN RAD A, SHARIYAT M. Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations[J]. Composite Structures, 2015, 125:558-574
[17] 洪轲,袁玲,沈中华, 等. Lamb波在含孔隙功能梯度材料中传播特性的研究[J]. 声学技术, 2012, 31(6):539-543 HONG Ke, YUAN Ling, SHEN Zhonghua, et al. Theoretical research on propagation characteristics of Lamb waves in porous FGMs[J]. Technical Acoustic, 2012, 31(6):539-543(in Chinese)
[18] FAHSI B, BOUIADJRA R B, MAHMOUDI A, et al. Assessing the effects of porosity on the bending, buckling, and vibrations of functionally graded beams resting on an elastic foundation by using a new refined quasi-3D theory[J]. Mechanics of Composite Materials,2019, 55(2):219-230
[19] WATTANASAKULPONG N, CHAROENSUK J. Vibration characteristics of stepped beams made of FGM using differential transformation method[J]. Meccanica, 2014, 50(4):1089-1101
[20] ELISHAKOFF I, PENTARAS D, GENTILINI C. Mechanics of functionally graded material structures[M]. Singapore:World Scientific Publishing Company, 2016
[21] ZHANG D, ZHOU Y. A theoretical analysis of FGM thin plates based on physical neutral surface[J]. Computational Materials Science, 2008, 44(2):716-720
[22] SRIDHAR A, SURIS Y B. Commutativity in Lagrangian and Hamiltonian mechanics[J]. Journal of Geometry and Physics, 2019, 137:154-161
[23] CHAKRAVERTY S, PRADHAN K K. Free vibration of functionally graded thin rectangular plates resting on Winkler elastic foundation with general boundary conditions using Rayleigh-Ritz method[J]. International Journal of Applied Mechanics, 2014, 6(4):1450043 |
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