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浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*

云天铨

云天铨. 浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*[J]. 应用数学和力学, 1989, 10(9): 759-766.
引用本文: 云天铨. 浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*[J]. 应用数学和力学, 1989, 10(9): 759-766.
Yun Tian-quan. Asymmetric Dynamic Instability of Axisymmetric Polar Dimpling of Thin Shallow Spherical Shells[J]. Applied Mathematics and Mechanics, 1989, 10(9): 759-766.
Citation: Yun Tian-quan. Asymmetric Dynamic Instability of Axisymmetric Polar Dimpling of Thin Shallow Spherical Shells[J]. Applied Mathematics and Mechanics, 1989, 10(9): 759-766.

浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*

基金项目: * 国家自然科学基金资助项目

Asymmetric Dynamic Instability of Axisymmetric Polar Dimpling of Thin Shallow Spherical Shells

  • 摘要: 当壳厚-升高比ε2<<1时,由二次型载荷产生的轴对称极凹陷的浅球薄壳是动力不稳定的.微小的扰动足以使它变成非轴对称凹陷.在两种情形下,问题都可归结为特征值问题Twn=cnwn.其中T当ε2<<1时近似为一Sfrum-Liouville算子.本文用谱理论和Hilbert定理均可证明T至少存在一实的特征值;它意味着轴对称极凹陷是动力不稳定的.再进一步,本文还找出代表不稳定凹陷壳体的非轴对称变形的、属于一特征值的T的特征函数.
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出版历程
  • 收稿日期:  1988-06-10
  • 刊出日期:  1989-09-15

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