非线性粘弹性梁的动力学行为

Dynamical Behavior of Nonlinear Viscoelastic Beams

建立了描述受周期荷载作用的均匀粘弹性梁动力学行为的非线性偏微分_积分方程 ,梁的材料满足Leaderman非线性本构关系 ,对于两端简支的情形用Galerkin方法进行了 2阶截断后 ,简化为常微分_积分方程 ,进一步简化为便于进行数值实验的常微分方程 ,最后用数值方法比较了 1阶和 2阶截断系统的动力学行为·

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 was 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 which is convenient to carry out numerical experiments. Finally, the dynamical behavior of 1_order and 2_order truncation are numerically compared.