Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid

NIE Qianjun; LI Lianhe

doi:10.21656/1000-0887.450327

Volume 47 Issue 1

Jan. 2026

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NIE Qianjun, LI Lianhe. Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid[J]. Applied Mathematics and Mechanics, 2026, 47(1): 46-56. doi: 10.21656/1000-0887.450327

Citation:

NIE Qianjun, LI Lianhe. Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid[J]. Applied Mathematics and Mechanics, 2026, 47(1): 46-56. doi: 10.21656/1000-0887.450327

Citation:

NIE Qianjun, LI Lianhe. Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid[J]. Applied Mathematics and Mechanics, 2026, 47(1): 46-56. doi: 10.21656/1000-0887.450327

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Transverse Vibration of Functionally Graded Material Cylinder Bars Dipped in Fluid

doi: 10.21656/1000-0887.450327

NIE Qianjun^1,2,3,
LI Lianhe^{1,2,3
,
,}

1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China;
2. Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China;
3. Key Laboratory of InfiniteDimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

Received Date: 2024-12-12
Rev Recd Date: 2025-04-22

Available Online: 2026-01-21

Publish Date: 2026-01-01

Abstract

Abstract

Based on the 1st-order shear deformation theory (FSDT) and the potential flow theory, the transverse vibration of functionally graded material (FGM) cylinder bars dipped in fluid was analyzed. The cermet bar material properties following a power-law distribution along the radial direction were represented by the radial gradient index. The fluid velocity potential and hydrodynamic loads were determined through solution of the Laplace equation in cylindrical coordinates with the variable separation method. The governing equations of motion were derived according to Hamilton’s principle. The fundamental frequencies and mode shapes were obtained with the generalized differential quadrature (GDQ) method and the direct iteration method. Additionally, the finite element analysis (CEL simulation) was used to validate the numerical results. Through parametric studies, the effects of the length-to-diameter ratio, the gradient index, the boundary conditions, as well as the fluid depth and density, on the transverse vibration behavior of the FGM bar-fluid interaction system were evaluated.
- FGM,
- transverse vibration,
- Hamilton’s principle,
- GDQ,
- fluid-structure interaction

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References(34)

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