Free vibration of a 2D-FGSW beam based on a shear deformation theory

Vu Thi An Ninh, Le Thi Ngoc Anh, Nguyen Dinh Kien
Author affiliations


  • Vu Thi An Ninh University of Transport and Communications, Hanoi, Vietnam
  • Le Thi Ngoc Anh Institute of Applied Mechanics and Informatics, Ho Chi Minh city, Vietnam
  • Nguyen Dinh Kien Institute of Mechanics, VAST, Hanoi, Vietnam



2D-FGSW beam, third-order shear deformation theory, transverse shear rotation, free vibration, finite element method


A two-dimensional functionally graded sandwich (2D-FGSW) beam model formed from three constituent materials is proposed and its free vibration is studied for the first time. The beam consists of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the length and thickness directions by power gradation laws. Based on a third-order shear deformation theory, a beam element using the transverse shear rotation as an independent variable is formulated and employed in the study. The obtained numerical result reveals that the variation of the material properties in the length direction plays an important role on the natural frequencies and vibration modes  of the beam. The effects of the material distribution and layer thickness ratio on the vibration characteristics are investigated in detail. The influence of the aspect ratio on the frequencies is also examined and discussed.


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How to Cite

V. T. A. Ninh, L. T. N. Anh and N. D. Kien, Free vibration of a 2D-FGSW beam based on a shear deformation theory, Vietnam J. Mech. 42 (2020) 189–205. DOI:



Research Article

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