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Title: On travelling wave modes of axially moving string and beam
Authors: Lu, L 
Yang, XD
Zhang, W
Lai, SK 
Issue Date: 2019
Source: Shock and vibration, 2019, v. 2019, 9496180, p. 1-13
Abstract: The traditional vibrational standing-wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time-varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n - 1 fixed nodes in the n(th) order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.
Publisher: Hindawi Publishing Corporation
Journal: Shock and vibration 
ISSN: 1070-9622
EISSN: 1875-9203
DOI: 10.1155/2019/9496180
Rights: Copyright © 2019 Lei Lu et al. This is an open access article distributed under the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The following publication Lu, L., Yang, X. D., Zhang, W., & Lai, S. K. (2019). On Travelling Wave Modes of Axially Moving String and Beam. Shock and Vibration, 2019, 9496180, 1-13 is available at
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