Abstract: 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.