Dynamical behavior of nonlinear viscoelastic columns based on 2-order galerkin truncation

Abstract

for a one-end clamped elastic beam has indicated that chaotic free-end motion obtained from an analog computer based on a one-mode Galerkin truncation is qualitatively consistent with the experimental measurements Ngl. The numerical research done by Abhyankar et al for a nonlinear simply-supported beam has shown that the numerical solutions of a parietal differential equation and a differential equation deduced by a single-mode Galerkin truncation yield similar results II9]. In addition to the direct comparison with numerical and experimental results, the suitability of the Galerkin truncation for researching on dynamical behavior of viscoelastic structures can be studied by comparing the dynamical behavior of different order truncation models simplified from a same mathematical model. In this paper, The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams is established . The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation that is convenient to carry out numerical experiments. Finally, the dynamical behaviors of l-order and 2-order truncated systems are numerically compared.