Instability of axially moving rectangular web with essential non homogeneous boundary conditions
Problems of stability of an axially moving elastic web, travelling between two rollers with constant velocity, and experiencing small transverse deformations (displacements) are considered in a 2-dimensional formulation with the help of non-homogeneous membrane model. To describe and analyze the instability process we perform the following decomposition and reduce analysis to two successively solved problems. The first problem consist in solution of in-plane equilibrium problem for the rectangular part of the continuous web with essentially nonlinear boundary conditions and finding the distributions of in-plane stresses. Using the obtained nonhomogeneous distributions the search of critical parameters of divergence and corresponding modes of instability (second problem) is formulated for the weak form of behaviour equation.