留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析

袁学刚 朱正佑 程昌钧

袁学刚, 朱正佑, 程昌钧. 具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析[J]. 应用数学和力学, 2005, 26(8): 892-898.
引用本文: 袁学刚, 朱正佑, 程昌钧. 具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析[J]. 应用数学和力学, 2005, 26(8): 892-898.
YUAN Xue-gang, ZHU Zheng-you, CHENG Chang-jun. Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell[J]. Applied Mathematics and Mechanics, 2005, 26(8): 892-898.
Citation: YUAN Xue-gang, ZHU Zheng-you, CHENG Chang-jun. Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell[J]. Applied Mathematics and Mechanics, 2005, 26(8): 892-898.

具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析

基金项目: 国家自然科学基金资助项目(10272069);上海市重点学科资助项目
详细信息
    作者简介:

    袁学刚(1971- ),男,吉林人,副教授,博士(E-mail:yxg1971@163.com);朱正佑(联系人.Tel:+86-21-56331454;E-mail:chjcheng@yc.shu.edu.cn).

  • 中图分类号: O175;O343

Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell

  • 摘要: 研究了一类具有缺陷的不可压缩超弹性材料球壳的径向对称运动问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压缩的neo-Hookean材料.得到了描述球壳内表面运动的二阶非线性常微分方程,并给出了方程的首次积分.通过对微分方程的解的动力学行为的分析,讨论了材料的缺陷参数和球壳变形前的内外半径的比值对解的定性性质的影响,并给出了相应的数值算例.特别地,对于一些给定的参数,证明了存在一个正的临界值,当内压与外压之差小于临界值时,球壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,球壳的内表面半径随时间的演化将无限增大,即球壳最终将被破坏.
  • [1] Ball J M.Discontinuous equilibrium solutions and cavitations in nonlinear elasticity[J].Philos Trans Roy Soc London,Ser A,1982,306(3):557—610. doi: 10.1098/rsta.1982.0095
    [2] Polignone D A,Horgan C O.Cavitation for incompressible anisotropic nonlinearly elastic spheres[J].Journal of Elasticity,1993,33(1):27—65. doi: 10.1007/BF00042634
    [3] Horgan C O, Polignone D A.Cavitation in nonlinearly elastic solids: a review[J].Applied Mechanics Review,1995,48(8):471—485. doi: 10.1115/1.3005108
    [4] 任九生、程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学,2002,23(8):783—788.
    [5] REN Jiu-sheng,CHENG Chang-jun.Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials[J].Journal Engineering Mathematics,2002,44(5):245—257. doi: 10.1023/A:1020910210880
    [6] SHANG Xin-chun,CHENG Chang-jun.Exact solution for cavitated bifurcation for compressible hyper-elastic materials[J].Internat J Engrg Sci,2001,39(12):1101—1117. doi: 10.1016/S0020-7225(00)00090-2
    [7] YUAN Xue-gang, ZHU Zheng-you. Qualitative analyses of spherical cavity nucleation and growth for incompressible generalized Valanis-Landel hyperelastic material[J].Acta Mechanica Solida Sinica,2004,17(2):158—165.
    [8] YUAN Xue-gang,ZHU Zheng-you,CHENG Chang-jun.Void Formation and growth for a class of compressible hyper-elastic sphere[J].Journal of Shanghai University,2004,8(1):13—19. doi: 10.1007/s11741-004-0004-8
    [9] YUAN Xue-gang,ZHU Zheng-you,CHENG Chang-jun.Cavitated formation and its vibration for a class of generalized incompressible hyper-elastic materials[J].Acta Mechanica Solida Sinica,2004,17(4):361—369.
    [10] Knowles J K.Large amplitude oscillations of a tube of incompressible elastic material[J].Quart Appl Math,1960,18(1):71—77.
    [11] Knowles J K.On a class of oscillations in the finite deformation theory of elasticity[J].J Appl Mech,1962,29(3):283—286. doi: 10.1115/1.3640542
    [12] Guo Z H,Solecki R.Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material[J].Arch Mech Stos,1963,15(8):427—433.
    [13] Calderer C.The dynamical behavior of nonlinear elastic spherical shells[J].J Elasticity,1983,13(1):17—47. doi: 10.1007/BF00041312
  • 加载中
计量
  • 文章访问数:  2676
  • HTML全文浏览量:  129
  • PDF下载量:  575
  • 被引次数: 0
出版历程
  • 收稿日期:  2003-12-20
  • 修回日期:  2005-03-22
  • 刊出日期:  2005-08-15

目录

    /

    返回文章
    返回