非线性粘弹性梁的动力学行为

基金项目: 国家自然科学基金项目(19727027);中国博士后科学基金项目(98JC14032);上海市科技发展基金项目(98SHB1417;98JC14032)

Dynamical Behavior of Nonlinear Viscoelastic Beams

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
2.
Department of Mechanics, Shanghai University, Shanghai 201800, P R China

摘要: 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。
- 粘弹性梁 /
- 运动微分方程 /
- Leaderman关系 /
- Galerkin方法
Abstract: 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.
- viscoelastic beam /
- differential equation of motion /
- Leaderman relation /
- Galerkin method

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