Research Papers

Vibrations and Stability of an Axially Moving Rectangular Composite Plate

[+] Author and Article Information
Xiao-Dong Yang1

Department of Engineering Mechanics, Shenyang Aerospace University, Shenyang 110136, Chinajxdyang@163.com

Li-Qun Chen

Department of Mechanics, Shanghai University, Shanghai 200436, China; Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Jean W. Zu

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada


Corresponding author.

J. Appl. Mech 78(1), 011018 (Oct 26, 2010) (11 pages) doi:10.1115/1.4002002 History: Received March 25, 2009; Revised June 02, 2010; Posted June 17, 2010; Published October 26, 2010; Online October 26, 2010

The vibrations and stability are investigated for an axially moving rectangular antisymmetric cross-ply composite plate supported on simple supports. The partial differential equations governing the in-plane and out-of-plane displacements are derived by the balance of linear momentum. The natural frequencies for the in-plane and out-of-plane vibrations are calculated by both the Galerkin method and differential quadrature method. It can be found that natural frequencies of the in-plane vibrations are much higher than those in the out-of-plane case, which makes considering out-of-plane vibrations only is reasonable. The instability caused by divergence and flutter is discussed by studying the complex natural frequencies for constant axial moving velocity. For the axially accelerating composite plate, the principal parametric and combination resonances are investigated by the method of multiple scales. The instability regions are discussed in the excitation frequency and excitation amplitude plane. Finally, the axial velocity at which the instability region reaches minimum is detected.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

The forces and moments acting on the element of the plate

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Figure 2

The natural frequencies for out-of-plane vibrations

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Figure 3

The natural frequencies for in-plane vibrations

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Figure 4

Natural frequencies for different width-length ratio

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Figure 5

The unstable regions of the parametric resonances

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Figure 6

The instability region width for different averaging velocities




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