A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges

YE Yunong; EBURILITU

doi:10.21656/1000-0887.450001

Volume 45 Issue 7

Jul. 2024

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YE Yunong, EBURILITU. A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges[J]. Applied Mathematics and Mechanics, 2024, 45(7): 898-906. doi: 10.21656/1000-0887.450001

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A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges

doi: 10.21656/1000-0887.450001

YE Yunong,
EBURILITU^,

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

Received Date: 2024-01-02
Rev Recd Date: 2024-01-31
Publish Date: 2024-07-01

Abstract

Abstract

The symplectic superposition method was used to study the vibration problem of the orthotropic rectangular thin plate point-supported at a corner and clamped at its opposite edges. Firstly, based on the boundary conditions, the original vibration problem was decomposed into 2 subproblems with 2 opposite edges simply supported. Next, the series expansion solutions to the 2 sub-vibration problems were obtained based on the separation variable method in the Hamiltonian system. Then the symplectic superposition solution to the original vibration problem was obtained with the superposition method. To determine the terms of the series expansion of the obtained symplectic superposition solution in specific calculations, the convergence analysis of the solution for calculating orthotropic rectangular thin plates was performed. The symplectic superposition solution was also used to calculate the vibration frequencies of the isotropic and orthotropic rectangular thin plate point-supported at a corner and clamped at its opposite edges, respectively, and to give the modes corresponding to the 1st 8 vibration frequencies of an orthotropic square thin plate.
- orthotropic rectangular thin plate,
- Hamiltonian system,
- symplectic superposition method,
- vibration

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References(19)

References

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