Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method

EBURILITU; FENG Lu; ALATANCANG

doi:10.21656/1000-0887.380092

Volume 39 Issue 3

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EBURILITU, FENG Lu, ALATANCANG. Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method[J]. Applied Mathematics and Mechanics, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092

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Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method

doi: 10.21656/1000-0887.380092

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²Huhhot University for Nationalities, Hohhot 010051, P.R.China

Funds: The National Natural Science Foundation of China(11362011;11371185;11761029)

Received Date: 2017-04-10
Rev Recd Date: 2017-05-04
Publish Date: 2018-03-15

Abstract

Abstract

The orthotropic rectangular thin plate equations were transformed into the Hamiltonian system, and the corresponding infinite dimensional Hamiltonian operator was obtained with the method of separation of variables. Then the eigenvalues and corresponding eigenfunctions of the Hamiltonian operator were calculated, and the eigenfunction system was proved to be of symplectic orthogonality and completeness. Finally, with the symplectic superposition method, the analytical bending solutions of fully clamped orthotropic rectangular thin plates were presented. The comparison between the analytical solutions and the numerical examples shows the correctness of the proposed method.
- orthotropic thin plate,
- infinite dimensional Hamiltonian operator,
- eigenfunction,
- analytical solution

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References(18)

References

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