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| Free vibration analysis for rectangular plates with variable thickness resting on a non-uniform Winkler elastic foundation by DTM |
| Received:February 17, 2017 Revised:May 20, 2017 |
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| DOI：10.7511/jslx20170217002 |
| KeyWord:non-uniform Winkler elastic foundations rectangular plates with variable thickness free vibration dimensionless natural frequency Differential Transformation Method (DTM) |
| Author | Institution |
| 滕兆春 |
兰州理工大学 理学院, 兰州 |
| 衡亚洲 |
兰州理工大学 理学院, 兰州 |
| 刘露 |
兰州理工大学 理学院, 兰州 |
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| Abstract: |
| For free vibration problem of rectangular plates with variable thickness resting on a non-uniform foundation and by an effective solving numerical method called differential transformation method (DTM),the dimensionless natural frequency characteristics are investigated.Two opposite edges of plates are assumed to be simply supported and other two edges can be changed into simply supported,camped or free boundary conditions arbitrarily.By using DTM,dimensionless normalized governing differential equation of rectangular plates with variable thickness resting on a non-uniform Winkler elastic foundation and boundary conditions are transformed to the equivalent algebraic equations,which can derive equations of dimensionless natural frequency.The example results are back to cases for uniform Winkler rectangular plates and rectangular plates with variable thickness,which are compared with different methods in present literature.The result shows that DTM have very higher accuracy and stronger applicability.Finally,the influence of the varied foundation parameter,the varied thickness parameter and the aspect ratio on dimensionless natural frequencies are analyzed for different boundary conditions and deriving the first six mode shapes for CSCS plate with variable thickness resting on a non-uniform Winkler elastic foundations. |