Research on Dispersion Characteristics of Multi-Segment Beam Lattices Based on the Dynamic Stiffness Theory and the Wittrick-Williams Algorithm

PENG Changqing; LIU Jinxing

doi:10.21656/1000-0887.450043

Volume 46 Issue 2

Feb. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(2): 154-164

PENG Changqing, LIU Jinxing. Research on Dispersion Characteristics of Multi-Segment Beam Lattices Based on the Dynamic Stiffness Theory and the Wittrick-Williams Algorithm[J]. Applied Mathematics and Mechanics, 2025, 46(2): 154-164. doi: 10.21656/1000-0887.450043

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Research on Dispersion Characteristics of Multi-Segment Beam Lattices Based on the Dynamic Stiffness Theory and the Wittrick-Williams Algorithm

doi: 10.21656/1000-0887.450043

PENG Changqing,
LIU Jinxing^,

Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R.China

Received Date: 2024-02-22
Rev Recd Date: 2024-03-18
Publish Date: 2025-02-01

Abstract

Abstract

The dynamic stiffness method (DSM) was employed to describe dynamic responses of periodic lattices composed of multi-segment beams (MSBs), and the dispersion characteristics were examined based on the Wittrick-Williams algorithm (WWA). First, the dynamic stiffness matrix of the MSB was obtained with the continuity conditions in terms of displacements and stresses at inner joints. The obtained dynamic stiffness matrix in nature remains a 2-node type element, and has the same dimensions as those of a 2-node homogeneous beam. The combination of the DSM and the WWA enables the accurate calculation of natural frequencies of the lattice. As for a periodic unit cell of the MSB lattice, the Floquet boundary condition was introduced into the initial DSM, and then dispersion curves and natural frequencies can were obtained with the WWA. In the irreducible Brillouin zone, results obtained with the proposed method agree reasonably well with those by software COMSOL, with errors no larger than 6%, which verifies the effectiveness of the proposed method. Furthermore, the effects of microscopic geometric and material parameters on lattice dispersion curves were studied. The results show that, the MSB makes an effective way to adjust dispersion characteristics of lattices by building periodic lattices.
- dynamic stiffness method,
- Wittrick-Williams algorithm,
- Floquet boundary condition,
- multi-segment beam lattice,
- dispersion curves

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References(23)

References

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