Free vibration of functionally graded beams resting on winkler foundation around the buckling domain

Abstract: 65 | PDF: 37

##plugins.themes.academic_pro.article.main##

Author

  • Huynh Vinh, Do Minh Duc

Keywords:

free vibration
FG beams
finite element method
critical buckling loads
Winkler foundation

Abstract

This paper investigates free vibration of functionally graded beams (FG beams) resting on Winkler foundation around the buckling domain. The governing equations of motion based on Euler–Bernoulli and Timoshenko beam theories together with Von Karman’s strain–displacement relation are derived from Lagrange’s equations. The material properties of the beams vary continuously in the thickness direction according to the power-law distributions. The finite element method is employed to discretize the model and obtain numerical approximations of the equilibrium equations. Numerical examples are carried out with the Matlab programming language. The reliability of the solution is verified by comparison with previously reported results in the literature. The effect of shear deformation, boundary conditions, and different material property distributions on the first frequency of the beams are also analyzed and discussed.

References

    [1] Chu Quốc Thắng, Phương pháp phần tử hữu hạn, Nhà xuất bản khoa học kỹ thuật, Hà Nội, 1997.
    [2] Đào Huy Bích, Nguyễn Đăng Bích, Cơ học môi trường liên tục, Nhà xuất bản xây dựng, Hà Nội, 2002
    [3] A. Shahba, S. Rajasekaran. “Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials”, Applied Mathematical Modelling, 36, 2012, pp. 3094–3111.
    [4] A. Shahba, R. Attarnejad, M. Tavanaie Marvi, S. Hajilar. “Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions”, Composites: Part B, 42, 2011, pp. 801–808.
    [5] A. Fallah, M.M. Aghdam. “Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation”, European Journal of Mechanics A/Solids, 30, 2011, pp. 571-583
    [6] A.S. Kanani, H. Niknam, A.R. Ohadi, M.M. Aghdam. “Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam”, Composite Structures, 115, 2014, pp. 60-68.
    [7] G.H. Rahimi, M.S. Gazor, M. Hemmatnezhad, H. Toorani. “On the post-buckling and free vibrations of FG Timoshenko beams”, Composite Structures, 95, 2013, pp. 247–253.
    [8] H.-T. Thai, T.P. Vo, “Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories”, International Journal of Mechanical Sciences, 62, 2012, pp. 57–66.
    [9] H.-S. Shen. Functionally graded materials: nonlinear analysis of plates and shells. Published by Taylor & Francis Group, LLC, 2009.
    [10] K.K. Pradhan, S. Chakraverty. “Effects of different shear deformation theories on free vibration of functionally graded beams”, International Journal of Mechanical Sciences, 82, 2014, pp. 149–160.
    [11] M. Aydogdu, V. Taskin. “Free vibration analysis of functionally graded beams with simply supported edges”, Material and Design, 28, 2007, pp. 1651–1656.
    [12] M. Simsek. “Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories”, Nuclear Engineering and Design, 240, 2010, pp. 697–705.
    [13] N. Wattanasakulpong, B. Gangadhara Prusty, D. W.Kelly. “Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams”, International Journal of Mechanical Sciences, 53, 2011, pp. 734–743
    [14] P. Tossapanon, N. Wattanasakulpong N. “Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation”, Composite Structures, 142, 2016, pp. 215–225.
    [15] S. Kumar, A. Mitra, H. Roy. “Geometrically nonlinear free vibration analysis of axially functionally graded taper beams”, Engineering Science and Technology, an International Journal, 18, 2015, pp. 579-593.
    [16] S-R. Li, RC. Batra. “Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler–Bernoulli beams”. Composite Structures, 95, 2013, pp.5–9
    [17] T-P.Vo, H-T. Thai, T-K.Nguyen, M. Alireza, J. Lee. “Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory” Engineering Structures, 64, 2014, pp. 12–22.
    [18] T-K. Nguyen, T-P. Vo, H-T. Thai. “Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory”, Composites: Part B, 55, 2013, pp. 147–157.
Read more

##plugins.themes.academic_pro.article.sidebar##

Published

Nov 30, 2017
Download
PDF
How to Cite
Huynh Vinh, Do Minh Duc. “Free Vibration of Functionally Graded Beams Resting on Winkler Foundation Around the Buckling Domain”. The University of Danang - Journal of Science and Technology, vol. 11, no. 120.4, Nov. 2017, pp. 104-9, https://jst-ud.vn/jst-ud/article/view/3767.

##plugins.themes.academic_pro.article.details##