Asymptotic behaviour of imperfect viscoelastic beams

In this paper the problem of the lateral stability of imperfect viscoelastic beams is analysed. The problem is examined by means of the quasi-static approach and leads to a system of integro-differential equations which can be resolved by a series expansions and the Laplace transforms. The viscous critical load is defined according to the asymptotic behaviour of the beam and can be evaluated by introducing the assumption of weak fading memory, solid material and thermodynamic compatibility. The critical load does not depend either on the type or the entity of the imperfections. Furthermore, some characteristic aspects of the problem, like the faster progress of the torque moment with respect to the progress of the lateral bending moment, are underlined. For a three-element model it is possible to reach a closed-form solution. In the case of the Poisson ratio constant in time and three-element model, an interesting analogy with the asymptotic behaviour of the imperfect column is observed.