Natural Vibration Frequencies of Laminated Composite Beams Based on the Scaled Boundary Finite Element Method

LI Wenwu; WANG Wei

doi:10.21656/1000-0887.440208

Volume 45 Issue 7

Jul. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(7): 936-948

LI Wenwu, WANG Wei. Natural Vibration Frequencies of Laminated Composite Beams Based on the Scaled Boundary Finite Element Method[J]. Applied Mathematics and Mechanics, 2024, 45(7): 936-948. doi: 10.21656/1000-0887.440208

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Natural Vibration Frequencies of Laminated Composite Beams Based on the Scaled Boundary Finite Element Method

doi: 10.21656/1000-0887.440208

LI Wenwu^{1
,
,},
WANG Wei^2
,

1.
Hunan Provincial Communications Planning, Survey & Design Insititute Co., Ltd., Changsha 410219, P.R.China
2.
Hunan Construction Investment Group, Changsha 410009, P.R.China

Received Date: 2023-07-10
Rev Recd Date: 2024-03-04
Publish Date: 2024-07-01

Abstract

Abstract

The scaled boundary finite element method (SBFEM) was extended to calculate the natural frequencies of laminated composite beams. With this method, the beam was simplified as a 1D model. Only the displacement components along the x and z directions were selected as the fundamental unknowns. Based on the fundamental equations of elasticity and the scaled boundary coordinates, under the principle of virtual work and with the dual vector technique, the 1st-order ordinary differential scaled boundary finite element dynamic equation for composite beams was obtained, with its general solution in the form of the analytical matrix exponential function. The Padé expansion was utilized to solve the matrix exponential function and the dynamic stiffness matrix for each beam layer was acquired. According to the principle of matching degrees of freedom, the global stiffness and mass matrices of the laminated beam were gained. The eigenvalue equation was solved to give the natural vibration frequencies of the laminated composite beam. The results show that, the proposed method is widely applicable without limitation on the layer number and boundary conditions. Comparisons between the numerical natural frequencies and the experiment results of 3-, 4- and 10-layered step-shaped cantilever beams, validate the accuracy, high efficiency and fast convergence of the SBFEM.
- laminate composite beam,
- natural frequency,
- scaled boundary finite element method (SBFEM),
- Padé expansion

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References(30)

References

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