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Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (1): 1-9.

• 组织与社会 •    下一篇

DYNAMICAL BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELLS UNDER AXIAL PRESSURES

程昌钧, 张能辉   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • 收稿日期:2000-03-21 修回日期:2000-08-29 出版日期:2001-01-18 发布日期:2001-01-18
  • 通讯作者: CHENG Chang-jun,Member of Editorial Committee,AMM
  • 基金资助:
    the National Natural Science Foundation of China (19772027); the Development Foundation of Shanghai Municipal Commission of Education (99A01); the Science Foundation of Shanghai Municipal Commission of Science and Technology (98JC14032); the Postdoctoral Science Foundation of Shanghai (1999 year)

DYNAMICAL BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELLS UNDER AXIAL PRESSURES

CHENG Chang-jun, ZHANG Neng-hui   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • Received:2000-03-21 Revised:2000-08-29 Online:2001-01-18 Published:2001-01-18
  • Supported by:
    the National Natural Science Foundation of China (19772027); the Development Foundation of Shanghai Municipal Commission of Education (99A01); the Science Foundation of Shanghai Municipal Commission of Science and Technology (98JC14032); the Postdoctoral Science Foundation of Shanghai (1999 year)

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摘要： The hypotheses of the Kármán-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Krmn equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such as, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.

关键词: Kármán-Donnell theory, viscoelastic cylindrical shell, chaos, hyperchaos, strange attractor, limit cycle

Abstract: The hypotheses of the Kármán-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Krmn equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such as, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.

Key words: Kármán-Donnell theory, viscoelastic cylindrical shell, chaos, hyperchaos, strange attractor, limit cycle

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