In-Plane Responses of Axially Moving Plates Subjected to Arbitrary Edge Excitations

The free and forced in-plane vibrations of axially
moving plates are investigated in this work. The plate possesses an
internal damping of which the constitutive relation obeys the
Kelvin-Voigt model, and the excitations are arbitrarily distributed on
two opposite edges. First, the equations of motion and the boundary
conditions of the axially moving plate are derived. Then, the extended
Ritz method is used to obtain discretized system equations. Finally,
numerical results for the natural frequencies and the mode shapes of
the in-plane vibration and the in-plane response of the moving plate
subjected to arbitrary edge excitations are presented. It is observed that
the symmetry class of the mode shapes of the in-plane vibration
disperses gradually as the moving speed gets higher, and the u- and
v-components of the mode shapes belong to different symmetry class.
In addition, large response amplitudes having shapes similar to the
mode shapes of the plate can be excited by the edge excitations at the
resonant frequencies and with the same symmetry class of distribution
as the u-components.

• T. H. Young
• Y. S. Ciou

• Arbitrary edge excitations
• axially moving plates
• in-plane vibration
• extended Ritz method.

<p>[1] F. Fung, J. S. Huang, and Y. C. Chen, &ldquo;The transient amplitude of the
viscoelastic travelling string: An integral constitutive law,&rdquo; Journal of
Sound and Vibration, vol. 201, pp. 153-167, 1997.
[2] L. Q. Chen, and X. D. Yang, &ldquo;Steady-state response of axially moving
viscoelastic beams with pulsating speed: comparison of two nonlinear
models,&rdquo; International Journal of Solids and Structures, vol. 42, pp.
35-50, 2005.
[3] C. Shin, J. Chung, and W. Kim, &ldquo;Dynamic characteristics of the
out-of-plane vibrations for an axially moving membrane,&rdquo; Journal of
Sound and Vibration, vol. 297, pp. 794-809, 2006.
[4] K. Marynowski, &ldquo;Two-dimensional rheological element in modeling of
axially moving viscoelastic web,&rdquo; European Journal of Mechanics &ndash;
A/Solids, vol. 25, pp. 729-744, 2006.
[5] C. C. Lin, &ldquo;Stability and vibration characteristics of axially moving
plates,&rdquo; International Journal of Solids and Structures, vol. 34, pp.
3179-3190, 1997.
[6] S. Hatami, H. R. Ronagh, and M. Azhari, &ldquo;Exact free vibration analysis of
axially moving viscoelastic plates,&rdquo; Computers &amp; Structures, vol. 86, pp.
1734-1746, 2008.
[7] K. Hyde, J. Y. Chang, C. Bacca, and J. A. Wickert, &ldquo;Parameter studies
for plane stress in-plane vibration of rectangular plates,&rdquo; Journal of
Sound and Vibration, vol. 247, pp. 471-487, 2001.
[8] J. Wauer, &ldquo;In-plane vibrations of rectangular plates under inhomogeneous
static edge load,&rdquo; European Journal of Mechanics &ndash; A/Solids, vol. 11, pp.
91-106, 1992.
[9] N. H. Farag, and J. Pan, &ldquo;Free and forced in-plane vibration of rectangular
plates,&rdquo; Journal of Acoustical Society of America, vol. 103, pp. 408-413,
1998.
[10] C. Shin, W. Kim, and J. Chung, &ldquo;Free in-plane vibration of an axially
moving membrane,&rdquo; Journal of Sound and Vibration, vol. 272, pp.
137-154, 2004.</p>