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| Analysis of free vibrations and critical buckling loads of a porous functionally graded materials rectangular plate resting on elastic foundation |
| Received:April 15, 2021 Revised:June 03, 2021 |
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| DOI：10.7511/jslx20210415003 |
| KeyWord:porous FGM rectangular plates Winkler elastic foundation porosity natural frequency critical buckling load Differential Transformation Method |
| Author | Institution |
| 滕兆春 |
兰州理工大学 理学院, 兰州 |
| 席鹏飞 |
兰州理工大学 理学院, 兰州 |
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| Abstract: |
| The properties of porous functionally graded materials (FGM) components are closely related to porosity and distribution form of the pores.Based on the classical plate theory,considering the modified mixing rate model with different pore distribution,the free vibration and critical buckling load of a porous FGM rectangular plate with four sides compression on Winkler elastic foundation are studied.Firstly,the Hamilton principle and the definition of the physical middle surface are used to derive the governing differential equation of the free vibration of the four-side compressed porous FGM rectangular plate on Winkler elastic foundation.Then the dimensionless form of the governing differential equation is also derived.The dimensionless governing differential equation and the boundary conditions are transformed by differential transformation method (DTM),and the algebraic characteristic equations for calculating the dimensionless natural frequencies and critical buckling loads are obtained.The problem is reduced to a FGM rectangular plate with zero porosity and compared with the existing literature to verify its effectiveness.Finally,the effects of gradient index,porosity,foundation stiffness coefficient,aspect ratio,compression load with four sides,boundary conditions on the dimensionless natural frequencies and all parameters on the dimensionless critical buckling loads of the porous FGM rectangular plate are calculated and analyzed. |
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