Theoretic Solution for Rectangular Thin Plate with Arbitrary Boundary Conditions By Symplectic Geometry Method
Zhong Yang(1,2),Zhang Yongshan(2)
(1 School of Civl. Engrg. Dalian University of Technology,Dalian 116024) (2 Dept . of Civl Engrg. Guangzhuo University Guangzhou 510405)

Abstract: The analytical solution for a rectangular thin plate with arbitrary boundary conditions is derived. The basic equations for elastic thin plate are tra nsformed into Hamilton canonical equations, And then the symplectic geometry met hod is adopted to separate the whole variables and the eigenvalues are obtained. According to the technology of eigen function expansion, the explicit solution can be presented. It is unnecessary to select the deformation function, thus the solution conforms to the requirement, a numerical example verifies the aualidity.
Keywords: rectangular thin plate, arbitrary boundary condition symplectic geometry, hamilton canonical equation.