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| Analytical solution for rectangular thin cantilever plate |
| Revised:June 03, 2004 |
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| DOI：10.7511/jslx20063068 |
| KeyWord:elastic rectangular thin cantilever plate,symplectic geometry,theoretial solution,hamilton canonical equations,variables separation |
| ZHONG Yang CHEN Jing-yun WANG Su-yan |
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| Abstract: |
| In this paper,the theoretial solution for the elastic cantilever rectangular thin plate is derived by symplectic geometry method.Firstly,the basic equations for elastic thin plate are transferred into Hamilton canonical equations.And then the whole variables are separated and also the eigenvalues are obtained by the symplectic geometry method.Finally,according to the method of eigen function expansion in the symplectic geometry,the explicit solutions for the elastic cantilever rectangular thin plate are presented.Due to the basic elasticity equations of the thin plate are only used and it is not needed prior to select the deformation function arbitrarily.Therefore,the solution is reasonable and theoretical.In order to proof the correcness of formulations,numerical results are also presented to comparing with that of the other reference. |
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