| 非线性粘弹性梁的动力学行为 |
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| 引用本文： | 陈立群,程昌钧.非线性粘弹性梁的动力学行为[J].应用数学和力学,2000,21(9):897-902. |
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| 作者姓名： | 陈立群 程昌钧 |
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| 作者单位： | 上海市应用数学和力学研究所,上海,200072;上海大学,力学系,上海,201800 |
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| 基金项目： | 国家自然科学基金项目 !(1972 70 2 7)，中国博士后科学基金项目!(98JC140 32 )，上海市科技发展基金项目 !(98SHB1417，98JC140 32 ) |
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| 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。
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| 关 键 词： | 运动微分方程 动力学行为 非线性粘弹性梁 |
Dynamical Behavior of Nonlinear Viscoelastic Beams |
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| CHEN Li-qun,CHENG Chang-jun.Dynamical Behavior of Nonlinear Viscoelastic Beams[J].Applied Mathematics and Mechanics,2000,21(9):897-902. |
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| Authors: | CHEN Li-qun CHENG Chang-jun |
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| 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. |
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| Keywords: | viscoelastic beam differential equation of motion Leaderman relation Galerkin method |
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