Stability of non-trivial equilibrium paths of beams on partial visco-elastic foundation

We consider a cantilever beam partially resting on a linear visco-elastic foundation of generalized Winkler type. The length and placement of the partial foundation are variable. The beam is subjected to a sub-tangential force at its unconstrained end. The stability of some of its non-trivial equilibrium configurations is investigated by a numerical procedure based on a finite differences technique. The critical boundaries of buckling and flutter are found; it turns out that the critical conditions for both static and dynamic instability depend on some physical parameters, and interactions between the boundaries of the domains of stability appear.