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

Yun Tian-quan

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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.

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.

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

Yun Tian-quan

Department of Mechanics, South China University of Technology, Guangzhou

Received Date: 1988-06-10
Publish Date: 1989-09-15

Abstract

Abstract

If the parameter ε², which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling of shallow spherical shell due to quadratic pressure distribution is dynamic instability, i.e., a small perturbation can change it to an asymmetric polar dimple mode.In two cases, the problem can be reduced to an eigenvalue problem Tw_n=c_n+w_n, where T can approximately be reduced to a Sturm-Liouvi/le operator if ε²<<1. The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, is 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.

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References(10)

References

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