Effects of the thickness on the stability of axially moving viscoelastic rectangular plates

The differential quadrature method is employed to solve the differential equation governing the in-plane moving rectangular viscoelastic plate with concave or convex cross sections. The boundary conditions of the plate are specified as simply supported-free (SFSF) and clamped-simply supported (CSCS). Plots showing the influence of the cross section's form on the plate's stability are presented and it is observed that the plate generally undergoes divergence instability but coupled mode instability also occurs for SFSF boundary conditions. Coupled mode instability appears when the cross-section is convex or varies linearly. Also, the increase of the thickness ratio plays an increasing role on the critical instability values of the moving speed.