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Stability analysis of an axially moving free-free beam

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Abstract

This study investigates the stability of an axially moving free-free beam as a function of moving speed, modulus of elasticity, and axial tensile force. The mode shapes of the beam under different axial tensile forces are also discussed. In this study, we derive the equations of motion of a flexible free-free beam with a uniformly circular cross section that moves axially at a constant speed. Using Galerkin’s technique, we dicretize and reduce the nonlinear partial differential equation of motion to a set of ordinary differential equations by choosing the shape functions to be the eigenfunctions of a free beam. The state-space method is used to investigate the stability of an axially moving free beam for different cases. Numerically, the stability of the system is influenced by different cases in various ways and degrees. The transverse vibration modes with different tensile forces are also considered in this study.

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Abbreviations

T :

Kinetic energy

V :

Potential energy

W :

Virtual work

p :

Mass density

E :

Young’s modulus

L :

Length of the beam

D :

External diameter of the beam

δ:

Wall thickness

P :

Constant axial tension

M :

Structural mass matrix

C :

Damping matrix

K :

Stiffness matrix

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Acknowledgments

This work was supported by a research program of the Heilongjiang Natural Science Foundation, China.

Author information

Authors and Affiliations

  1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin City, Heilongjiang Province, China

    Han Guangcai & Liu Fei

  2. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin City, Heilongjiang Province, China

    Wu Yanhong & Wang Wei

Authors
  1. Han Guangcai
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  2. Liu Fei
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  3. Wu Yanhong
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  4. Wang Wei
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Corresponding author

Correspondence to Liu Fei.

Additional information

Han Guangcai, Ph.D., was born in 1966 and is a Professor of Engineering Mechanics at the College of Aerospace and Civil Engineering, Harbin Engineering University. He engages in vibration active control and multibody system dynamics of theoretical teaching and research. His major academic achievements include dynamic behavior research on the coupling of rigid-flexible rotating blade, fuzzy and sliding mode control of thin plate vibration, active vibration control of actuators on ships, energy equation of higher-order mechanical systems, solving elastic mechanics using the Hamilton method, finite element calculation, and dynamic analysis and testing of armored tracked vehicles.

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Guangcai, H., Fei, L., Yanhong, W. et al. Stability analysis of an axially moving free-free beam. J Mech Sci Technol 34, 1821–1829 (2020). https://doi.org/10.1007/s12206-020-0402-2

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  • DOI: https://doi.org/10.1007/s12206-020-0402-2

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