Free Vibration Analysis of Functionally Graded Timoshenko Beams with Variable Section

被引：0
|
作者：
Du Y. [1 ]
Cheng P. [1 ]
Zhou F. [1 ]
机构：
[1] College of Civil Engineering, Hunan University, Changsha
来源：
Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences | 2021年 / 48卷 / 05期
关键词：
FGM beams; Free vibration; Physical neutral surface; Power series solution; Timoshenko beam;
D O I：
10.16339/j.cnki.hdxbzkb.2021.05.007
中图分类号：
TU3 [建筑结构];
学科分类号：
081304 ; 081402 ;
摘要：
Based on the concept of physical neutral surface, the governing differential equations of free vibration of an axial-loaded functionally graded material (FGM) beam with the material properties varying along the beam height are derived by using Hamilton principle, and then the power series solutions of the differential equations are obtained. Then, the frequency equation is obtained based on the general boundary conditions expressed by elastic constraints. The effects of the parameters such as the length-height ratio, the gradient index, the axial force, and the section variation coefficient on the natural vibration characteristics of functionally graded beams are analyzed. The results show that the shear deformation affects not only the flexural vibration but also the axial vibration. © 2021, Editorial Department of Journal of Hunan University. All right reserved.
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页码：55 / 62
页数：7
相关论文
共 18 条
  • [1] LONG S Y, LIU K Y, LI G Y., A meshless local radial point interpolation method for the analysis of functionally graded materials, Journal of Hunan University (Natural Sciences), 34, 3, pp. 41-44, (2007)
  • [2] YANG X J, XU H B, ZHENG J., ICM topology optimization method of functionally graded structures considering displacement constraint, Journal of Hunan University(Natural Sciences), 44, 4, pp. 56-62, (2017)
  • [3] YANG J, CHEN Y., Free vibration and buckling analyses of functionally graded beams with edge cracks, Composite Structures, 83, 1, pp. 48-60, (2008)
  • [4] SIMSEK M, KOCATURK T., Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures, 90, 4, pp. 465-473, (2009)
  • [5] LEE J W, LEE J Y., Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122, pp. 1-17, (2017)
  • [6] GONG Y., Analysis of bending, buckling and free vibration of functionally graded materials beam, pp. 9-26, (2009)
  • [7] LEE J W, LEE J Y., Contribution rates of normal and shear strain energies to the natural frequencies of functionally graded shear deformation beams, Composites Part B: Engineering, 159, pp. 86-104, (2019)
  • [8] PU Y, TENG Z C., Free vibration of FGM beams based on the first-order shear deformation theory by a modified generalized differential quadrature method, Journal of Vibration and Shock, 37, 16, pp. 212-218, (2018)
  • [9] PRADHAN K K, CHAKRAVERTY S., Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams, Applied Mathematics and Computation, 268, pp. 1240-1258, (2015)
  • [10] SIMSEK M., Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, 240, 4, pp. 697-705, (2010)
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