Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

HOU Guo-lin; Alatancang

doi:10.3879/j.issn.1000-0887.2010.10.005

Volume 31 Issue 10

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HOU Guo-lin, Alatancang. Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1181-1190. doi: 10.3879/j.issn.1000-0887.2010.10.005

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Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

doi: 10.3879/j.issn.1000-0887.2010.10.005

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2010-09-03
Publish Date: 2010-10-15

Abstract

Abstract

The eigenvalue problem of the Hamiltonian operator associated with the plane elasticity problems was investigated.First, the eigenfunctions of the operator with the mixed boundary conditions for the displacement and stress in the rectangular region was solved directly.Then, the completeness of the eigenfunctions was proved, thereby demonstrating the feasibility of using separation of variables to solve the problems.Finally, the general solution was obtained by using the symplectic eigenfunction expansion theorem.
- plane elasticity problems,
- Hamiltonian system,
- symplectic orthogonality,
- eigenfunction expansion,
- Hamiltonian operator

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References(14)

References

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