不可压缩层合橡胶圆管径向膨胀的稳定性分析  

Stability Analysis of Radial Inflation of Incompressible Composite Rubber Tubes

作　　者：袁学刚[1,2] 张文正[2] 张洪武[2] 朱正佑[3] 

机构地区：[1]大连民族学院理学院,辽宁大连116600 [2]大连理工大学工业装备结构分析国家重点实验室工程力学系,辽宁大连116024 [3]上海大学力学系上海市应用数学和力学研究所,上海200072

出　　处：《应用数学和力学》2011年第3期286-292,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1087204510721062);教育部优秀人才支持计划基金资助项目(NCET-09-096);中央高校基本科研业务费专项基金资助项目(DC10030104)

摘　　要：研究由两类不可压缩的橡胶材料组成的层合圆柱形管道,在内表面受到突加的径向压力作用时的膨胀机理.建立了问题的数学模型;利用材料的不可压缩条件、边界条件以及圆管的径向位移和径向应力的连续性条件将相应的控制方程约化为一个二阶非线性常微分方程,并得到了该方程的首次积分.给出了管道拟静态膨胀和动态膨胀的定性分析,特别地,结合数值算例讨论了材料参数、结构参数以及径向压力对管道径向膨胀和非线性周期振动的影响.The inflation mechanism was examined for a composite cylindrical tube composed of two incompressible rubber materials,where the inner surface of the tube was subjected to a suddenly applied radial pressure.The mathematical model of the problem was formulated and the corresponding governing equation was reduced to a second order ordinary differential equation by using the incompressible condition of the material,the boundary conditions and the continuity conditions of radial displacement and radial stress of the cylindrical tube,moreover,the first integral of the equation was obtained.The qualitative analyses of static inflation and dynamic inflation of the tube were presented,particularly,the effects of material parameters,structure parameters and radial pressure on radial inflation and nonlinearly periodic oscillation of the tube were discussed by combining numerical examples.

关 键 词：层合橡胶管道 径向膨胀 稳定性 非线性周期振动 

分 类 号：O343[理学—固体力学]