Dynamical Behavior of Nonlinear Viscoelastic Beams

The integro_partial_differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was 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 2nd_order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of 1st_order and 2nd_order truncation are numerically compared.