Natural frequencies,modes and critical speeds of axially moving Timoshenko beams with different boundary conditions |
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Authors: | You-Qi Tang Li-Qun Chen Xiao-Dong Yang |
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Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China;2. Department of Mechanics, Shanghai University, 99 Shang Da Road, Shanghai 200436, China;3. Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang 110136, China;1. School of Astronautics, Harbin Institute of Technology, P.O. Box 137, Harbin 150001, China;2. College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China |
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Abstract: | In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton's second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated. |
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