Problems with the Toeplitz and quasi-Toeplitz matrices that appear in the static stability analysis of elastic systems

Three stability problems are considered for layered elastic systems. The problems can be treated completely analytically. These systems are packs consisting of arbitrary numbers of identical infinite plates attached by identical layers of a soft medium modelled as a Winkler foundation. The problems differ in the nature of the boundary conditions assigned to the faces of the packets. Each face can be either free, or attached to a non-deformable support. A cylindrical corrugation is sought everywhere. In all cases the critical force, the whole load spectrum and all the forms of stability loss are given by simple explicit formulae.