Techno Press

Steel and Composite Structures   Volume 29, Number 3, November10 2018, pages 363-377
Free vibration of tapered BFGM beams using an efficient shear deformable finite element model
Dinh Kien Nguyen and Thi Thom Tran

Abstract     [Full Text]
    An efficient and free of shear locking finite element model is developed and employed to study free vibration of tapered bidirectional functionally graded material (BFGM) beams. The beam material is assumed to be formed from four distinct constituent materials whose volume fraction continuously varies along the longitudinal and thickness directions by power-law functions. The finite element formulation based on the first-order shear deformation theory is derived by using hierarchical functions to interpolate the displacement field. In order to improve efficiency and accuracy of the formulation, the shear strain is constrained to constant and the exact variation of the cross-sectional profile is employed to compute the element stiffness and mass matrices. A comprehensive parametric study is carried out to highlight the influence of the material distribution, the taper and aspect ratios as well as the boundary conditions on the vibration characteristics. Numerical investigation reveals that the proposed model is efficient, and it is capable to evaluate the natural frequencies of BFGM beams by using a small number of the elements. It is also shown that the effect of the taper ratio on the fundamental frequency of the BFGM beams is significantly influenced by the boundary conditions. The present results are of benefit to optimum design of tapered FGM beam structures.
Key Words
    bi-directional functionally graded material; tapered beams; first-order shear deformation theory; hierarchical functions; free vibration; finite element model
(1) Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam;
(2) Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam.

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