Free Vibration and Buckling Analyses of Functionally Graded Porous Columns by FEM

Lan Hoang Ton That


This article presents the free vibration and buckling behaviors of functionally graded porous (FGP) columns by using FEM (finite element method). The Matlab code developed based on the finite element formulation is validated by solving the above problems under four types of boundary condition. Numerical results which are in terms of natural frequencies and buckling load are compared with the analytical solutions and further extended to FGP columns. Besides, some mode shapes of this structure are also depicted in this article to provide specific views about the free vibration and buckling behaviors of the proposed structure.


Buckling; Column; Finite element method; Free vibration; Functionally graded porous.

Article Metrics

Abstract view : 50 times
PDF - 17 times

Full Text:



R. M. Mahamood and E.T. Akinlabi, Functionally Graded Materials. Springer International Publishing, 2017.

K. Ichikawa, Functionally Graded Materials in the 21st Century: A Workshop on Trends and Forecasts. Springer USA, 2001.

A. Öchsner, G. E. Murch and M. J. S. de Lemos, Cellular and Porous Materials: Thermal Properties Simulation and Prediction. Wiley, 2008.

Z. Liu, Multiphysics in Porous Materials. Springer International Publishing, 2018.

B. Akgöz and Ö. Civalek, A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science, 70, 2013, 1-14.

M. Şimşek and J. N. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Science, 64, 2013,


M. Şimşek and H. H. Yurtcu, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures, 97, 2013, 378-386.

D. S. Mashat, E. Carrera, A. M. Zenkour, S. A. Al Khateeb and M. Filippi, Free vibration of FGM layered beams by various theories and finite elements, Composites Part B: Engineering, 59, 2014, 269-278.

S. S. Kolukula, Available from:

D. -Q. Vo, and H. L. Ton-That, Free vibration of simply supported steel I-girders with trapezoidal web corrugations, Reports in Mechanical Engineering, 1(1), 2020, 141-150.

H. L. Ton-That, Plate structural analysis based on a double interpolation element with arbitrary meshing, Acta Mechanica et Automatica, 15(2), 2021, 91-99.

M. J. Aubad, S. O. W. Khafaji, M. T. Hussein and M. A. Al-Shujairi, Modal analysis and transient response of axially functionally graded (AFG) beam using finite element method. Materials Research Express, 6(10), 2019, 10654.

Y. Yang, C. C. Lam, K. P. Kou and V. P. Iu, Free vibration analysis of the functionally graded sandwich beams by a meshfree boundary-domain integral equation method, Composite Structures, 117, 2014, 32-39.

M. Chehel Amirani, S. M. R. Khalili and N. Nemati, Free vibration analysis of sandwich beam with FG core using the element free Galerkin method, Composite Structures, 90(3), 2009, 373-379.

N.T. Giang, Free vibration exploration of rotating FGM porosity beams under axial load considering the initial geometrical imperfection, Mathematical Problems in Engineering, 2021, 5519946.

H. L. That Ton, A study of functionally graded porous beam based on simple beam theory, International Journal of Engineering and Applied Physics, 1(3), 2021, 226-234.

L. H. That Ton, Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory Technical Journal of Daukeyev University, 2(1), 2022, 1-10.

L. H. Donnell, Beams, Plates and Shells. McGraw-Hill, 1976.

S. Timoshenko, Strength of Materials: Elementary Theory and Problems, R. E. Krieger Publishing Company, 1976.

S. Timoshenko, Theory of Elasticity, McGraw-Hill Education (India), 2010.


  • There are currently no refbacks.