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

动载荷下不可压缩超弹性球形薄膜的若干定性性质

袁学刚 张洪武 任九生 朱正佑

袁学刚, 张洪武, 任九生, 朱正佑. 动载荷下不可压缩超弹性球形薄膜的若干定性性质[J]. 应用数学和力学, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
引用本文: 袁学刚, 张洪武, 任九生, 朱正佑. 动载荷下不可压缩超弹性球形薄膜的若干定性性质[J]. 应用数学和力学, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you. Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads[J]. Applied Mathematics and Mechanics, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
Citation: YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you. Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads[J]. Applied Mathematics and Mechanics, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011

动载荷下不可压缩超弹性球形薄膜的若干定性性质

doi: 10.3879/j.issn.1000-0887.2010.07.011
基金项目: 国家自然科学基金资助项目(10872045;10721062;10772104);教育部优秀人才支持计划资助项目(CNET-09-096);中国博士后科学基金资助项目(20070421049);中央高校基本科研业务费专项资金资助项目(DC10030104)
详细信息
    作者简介:

    袁学刚(1971- ),男,吉林桦甸人,教授,博士(联系人.E-mail:yxg1971@163.com).

  • 中图分类号: O343

Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads

  • 摘要: 对于由横观各向同性不可压缩的Rivlin-Saunders材料组成的球形薄膜,研究了薄膜的内、外表面在周期阶梯载荷作用下的轴对称变形的非线性动力学特性.通过令球形结构的厚度趋近于1,得到了近似描述薄膜径向对称运动的二阶非线性常微分方程.详细讨论了解的定性性质.特别地,给出了球形薄膜随时间的运动产生非线性周期振动的可控性条件,证明了在某些情形下周期振动的振幅会出现“∞”型同宿轨道以及周期振动的振幅会出现不连续增长现象,并给出了相应的数值模拟.
  • [1] Beatty M F. Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues—with examples [J]. Applied Mechanics Review, 1987, 40(12): 1699-1733. doi: 10.1115/1.3149545
    [2] Fu Y B, Ogden R W. Nonlinear Elasticity: Theory and Applications[M].Cambridge: Cambridge University Press, 2001.
    [3] Knowles J K. Large amplitude oscillations of a tube of incompressible elastic material [J]. Q Appl Math, 1960, 18(1): 71-77.
    [4] Guo Z H, Solecki R. Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material [J]. Arch Math Stos, 1963, 15(8): 427-433.
    [5] Calderer C. The dynamical behavior of nonlinear elastic spherical shells [J]. J Elasticity, 1983, 13(1): 17-47. doi: 10.1007/BF00041312
    [6] 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.
    [7] Verron E, Khayat R E, Derdouri A, Peseux B. Dynamic inflation of hyperelastic spherical membranes [J]. Inc J Rheol, 1999, 43(5): 1083-1097. doi: 10.1122/1.551017
    [8] Chou-Wang M-S, Horgan C O. Cavitation in nonlinearly elastodynamics for neo-Hookean materials [J]. Int J Engin Sci, 1989, 27(8): 967-973. doi: 10.1016/0020-7225(89)90037-2
    [9] REN Jiu-sheng, CHENG Chang-jun. Dynamical formation of cavity in transversely hyperelastic spheres [J]. Acta Mechanica Sinica, 2003, 19(4): 320-323. doi: 10.1007/BF02487808
    [10] YUAN Xue-gang, ZHU Zheng-you, ZHANG Ruo-jing. Cavity formation and singular periodic oscillations in isotropic incompressible hyperelastic materials [J]. Int J Nonlinear Mech, 2006, 41(2): 294-303. doi: 10.1016/j.ijnonlinmec.2005.08.001
    [11] YUAN Xue-gang, ZHANG Hong-wu. Nonlinear dynamical analysis of cavitation in anisotropic incompressible hyperelastic spheres under periodic step loads [J]. Computer Modeling in Engineering & Sciences, 2008, 32(3): 175-184.
    [12] 任九生. 周期荷载下超弹性圆柱壳的动力响应 [J]. 应用数学和力学, 2008, 29(10): 1199-1207.
    [13] Polignone D A, Horgan C O. Cavitation for incompressible anisotropic nonlinearly elastic spheres [J]. J Elasticity, 1993, 33(1): 27-65. doi: 10.1007/BF00042634
    [14] Rivlin R S D, Saunders W. Large elastic deformations for isotropic materials—Ⅶ experiments on the deformation of rubbers [J]. Philos Trans Roy Soc Lond Ser A, 1951, 243(865): 251-288. doi: 10.1098/rsta.1951.0004
    [15] Gent A N, Thomas J. Forms for the stored energy function for vulcanized rubber [J]. J Polym Sci, 1958, 28(118): 625-628. doi: 10.1002/pol.1958.1202811814
  • 加载中
计量
  • 文章访问数:  1253
  • HTML全文浏览量:  88
  • PDF下载量:  795
  • 被引次数: 0
出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-05-12
  • 刊出日期:  2010-07-15

目录

    /

    返回文章
    返回