Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

FAN Junjie; LI Lianhe; ALATANCANG

doi:10.21656/1000-0887.430267

Volume 44 Issue 7

Jul. 2023

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FAN Junjie, LI Lianhe, ALATANCANG. Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported[J]. Applied Mathematics and Mechanics, 2023, 44(7): 834-846. doi: 10.21656/1000-0887.430267

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Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

doi: 10.21656/1000-0887.430267

FAN Junjie^{1, 2, 3
,},
LI Lianhe^{1, 2, 3
,},
ALATANCANG^{1, 2, 3
,
,}

1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China
3.
Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

Received Date: 2022-08-29
Rev Recd Date: 2022-10-21
Publish Date: 2023-07-01

Abstract

Abstract

The symplectic method for the elastic problem of decagonal symmetric 2D quasicrystal plates with 2 opposite edges simply supported, was discussed. The basic equations of the elastic theory for decagonal symmetric 2D quasicrystals were transformed into the Hamilton dual equations. With the method of separation of variables, the symplectic eigenvalues of the corresponding Hamilton operator matrix and the symplectic eigenfunction system were obtained. The completeness of the symplectic eigenfunction system of the Hamilton operator matrix in the sense of the Cauchy principal value was proved. Based on the symplectic eigenfunction expansion of the Hamilton system, the analytical solution to the bending problem of the decagonal symmetric 2D quasicrystal plate was given.
- decagonal symmetric 2D quasicrystal,
- symplectic method,
- Hamilton canonical equation,
- completeness

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References(34)

References

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