Fugue Effect on Bending of Nonlinear Viscoelastic Beams

Based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for the bending of nonlinear viscoelastic beams was established in this paper. The Laplace transformation method and the Titchmarsh theorem were used to prove that some relations exist between solutions to bending problems of visco- and elastic beams, which reveals the fugue effect of viscoelastic materials. The high-order Galerkin approximate solution to the quasi-static response of nonlinear viscoelastic beams under a step load was obtained by using the new method suggested in this paper as well as the Mathematica software and the Newton iteration technique.