ASYMMETRIC DYNAMIC INSTABILITY OF AXISYMMETRIC POLAR DIMPLING OF THIN SHALLOW SPHERICAL SHELLS  

作　　者：云天铨 

机构地区：[1]Department of Mechanics,South China University of Technology, Guangzhou

出　　处：《Applied Mathematics and Mechanics(English Edition)》1989年第9期797-804,共8页应用数学和力学（英文版）

基　　金：The Project Supported by National Natural Science Foundation of China;This paper was accepted to present at ICTAM 88(Grenoble)

摘　　要：If the parameter , which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling oj .shallow .spherical .shell due to quadratic pressure distribution i.s dynamic instability, i.e., a small perturbation can change il to an asymmetric polar dimple mode. In two cases, the problem can be reduced to an eigenvalue problem where T can approximately be reduced to a Sturm-Liouvi/le operator if The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, i.s proved by spectral theorem or Hilbert theorem. Furthermore, an eigenfunction, which represents one of the asymmetric modes of the unstable dimple shell, belonging to an eigenvalue of T, is found.If the parameter , which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling oj .shallow .spherical .shell due to quadratic pressure distribution i.s dynamic instability, i.e., a small perturbation can change il to an asymmetric polar dimple mode. In two cases, the problem can be reduced to an eigenvalue problem where T can approximately be reduced to a Sturm-Liouvi/le operator if The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, i.s proved by spectral theorem or Hilbert theorem. Furthermore, an eigenfunction, which represents one of the asymmetric modes of the unstable dimple shell, belonging to an eigenvalue of T, is found.

关 键 词：ASYMMETRIC DYNAMIC INSTABILITY OF AXISYMMETRIC POLAR DIMPLING OF THIN SHALLOW SPHERICAL SHELLS 

分 类 号：O3，O1[理学—力学]