A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges
A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges
The symplectic superposition method was used to study the vibration problem of the orthotropic rec-tangular thin plate point-supported at a corner and clamped at its opposite edges.Firstly,based on the bounda-ry 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 solu-tion 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.
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