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Research Papers

# Dynamic Stability of Cracked Viscoelastic Rectangular Plate Subjected to Tangential Follower Force

[+] Author and Article Information
Zhong-min Wang, Yan Wang, Yin-feng Zhou

School of Sciences, Xi’an University of Technology, Xi’an 710054, P.R.C.

J. Appl. Mech 75(6), 061018 (Aug 21, 2008) (12 pages) doi:10.1115/1.2936927 History: Received April 16, 2007; Revised March 27, 2008; Published August 21, 2008

## Abstract

Based on the thin plate theory and the two-dimensional viscoelastic differential type constitutive relation, the differential equation of motion of a viscoelastic plate containing an all-over part-through crack and subjected to uniformly distributed tangential follower force is established in Laplace domain. Then, by performing the Laplace inverse transformation, the differential equation of motion of the plate in the time domain is obtained. The expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are obtained by the differential quadrature method, and the $δ$ method is adopted at the crack continuity conditions. The general eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force under the different boundary conditions are calculated. The transverse vibration characteristics, type of instability, and corresponding critical loads of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are analyzed.

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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

The cracked viscoelastic rectangular plate subjected to uniformly distributed tangential follower forces

Figure 2

The first dimensionless complex frequency varied with the crack depth at different crack locations (c=1.0, H→0)

Figure 5

The first dimensionless complex frequency varied with the crack depth (c=1.0, H=10−3, q=50)

Figure 6

The second dimensionless complex frequency varied with the crack depth (c=1.0, H=10−3, q=50)

Figure 3

The second dimensionless complex frequency varied with the crack depth at different crack locations (c=1.0, H→0)

Figure 4

The real part of the first two order dimensionless frequency ratio: (a) first and (b) second versus the crack depth for various crack locations (c=1.0, H=10−3)

Figure 17

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−3, c=2.0)

Figure 18

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=5×10−3, c=1.0, s=0)

Figure 19

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=5×10−3, c=1.0, s=0.5, ξ=0.288)

Figure 7

The first three order dimensionless complex frequencies versus dimensionless follower force q (c=1.0, H=10−3)

Figure 8

The first three order dimensionless complex frequencies versus dimensionless follower force q (c=1.5, H=10−3)

Figure 9

The first three order dimensionless complex frequencies versus dimensionless follower force q (c=2.0, H=10−3)

Figure 10

The real part of the first two order dimensionless frequency ratio: (a) first and (b) second versus the crack depth for various crack locations (c=1.0, H=10−3)

Figure 11

The first dimensionless complex frequency varied with the crack depth (H=10−3)

Figure 12

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−5, c=1.0)

Figure 13

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−3, c=1.0)

Figure 14

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−5, c=1.5)

Figure 15

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−3, c=1.5)

Figure 16

The first three order dimensionless complex frequencies versus dimensionless follower force q (H=10−5, c=2.0)

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