Stability of a compressed nonlocally viscoelastic beam lying on an elastic base

Abstract

The paper deals with the stability of an infinitely long beam lying on a solid elastic base and subjected to a constant or time-periodically varying longitudinal force. The beam material is characterized by nonlocally viscoelastic properties. Stability is understood as asymptotic stability in the sense of Lyapunov. The influence of the loading parameters and the parameters characterizing the nonlocal viscoelastic properties of the beam material on buckling and stability is analyzed. Stability is analyzed by using the maximum Lyapunov exponent.