Journal
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Volume 50, Issue 10-11, Pages 1448-1458Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmecsci.2008.09.001
Keywords
Axially moving beams; Timoshenko model; The complex mode approach; Modes; Natural frequencies; Critical speeds
Categories
Funding
- National Outstanding Young Scientists Fund of China [10725209]
- National Natural Science Foundation of China [10672092]
- Shanghai Municipal Education Commission Scientific Research [07ZZ07]
- Shanghai University [A.16-0401-08-005]
- Shanghai Leading Academic Discipline Project [Y0103]
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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. (c) 2008 Elsevier Ltd. All rights reserved.
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