Stability of a non-uniform beam on a viscoelastic foundation with a shear layer subjected to a non-conservative force

The stability of a cantilever beam of linearly variable rectangular cross-section lying on a viscoelastic foundation with a shear layer subjected to a circulatory force at its free end is investigated. The materials of the beam and the foundation are assumed to be Kelvin-type solids. Approximate values of the critical loads are calculated on the basis of an adjoint variational principle. The influence of geometric and material properties of the system on the critical load is depicted through several graphs. It is found that a shear layer may destabilize the system in certain cases.