Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes

GUAN Yuming; GE Xinsheng

doi:10.21656/1000-0887.420089

Volume 43 Issue 2

Feb. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(2): 156-165

GUAN Yuming, GE Xinsheng. Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes[J]. Applied Mathematics and Mechanics, 2022, 43(2): 156-165. doi: 10.21656/1000-0887.420089

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Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes

doi: 10.21656/1000-0887.420089

GUAN Yuming,
GE Xinsheng^,

College of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, P.R.China

Received Date: 2021-04-07
Rev Recd Date: 2022-01-06

Available Online: 2022-01-11

Publish Date: 2022-02-01

Abstract

Abstract

The transverse deformation of the beam will lead to the longitudinal shortening deformation, and this transverse-longitudinal deformation coupling will bring the dynamic stiffening effect term on the generalized rigidity of the beam model. For the rotating beam structure, the centrifugal force will cause axial tension, with coupling axial and transverse deformation of the beam and bring additional geometric stiffness, which is more obvious for the thick short beam. The central rigid body-Timoshenko beam model with a large-range-motion center was investigated. Firstly, the dynamic model with centrifugal forces was established by means of the Timoshenko beam theory and the Hamilton principle. Secondly, the unconstrained mode concept was introduced, and the unconstrained mode shape functions and natural frequencies were solved with the Frobenius method. Finally, numerical simulations were carried out to explore the difference of generalized stiffness between the unconstrained mode and the constrained mode at different constant speeds, and the effects of centrifugal forces on the model under unconstrained mode condition were discussed.
- rigid-flexible coupling,
- dynamic stiffening,
- Timoshenko beam,
- unconstrained mode

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References(28)

References

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