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| Free vibration analysis of porous functionally graded materials Timoshenko beam |
| Received:August 04, 2020 Revised:December 30, 2020 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20200804002 |
| KeyWord:functionally graded materials beam porosity free vibration natural frequency Differential Transformation Method |
| Author | Institution |
| 王伟斌 |
兰州理工大学 理学院, 兰州 |
| 杨文秀 |
兰州理工大学 理学院, 兰州 |
| 滕兆春 |
兰州理工大学 理学院, 兰州 |
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| Abstract: |
| The free vibration of beam made from porous functionally graded materials (FGMs) is studied based on the theory of Timoshenko beam.Firstly, two types of pore distributions are established by considering the porosity model of the porous functionally graded material.Secondly, based on the theory of Timoshenko beam, displacement equation, geometric equation and constitutive equations, using the Hamilton principle, the governing differential equation of free vibration for porous functional gradient material beams is derived.Its dimensionless form is also obtained.Then through the application of differential transformation method (DTM) to the dimensionless governing differential equations and boundary conditions of transformation, the equivalent algebraic characteristics equations about the natural frequencies are obtained.Finally, the dimensionless natural frequencies of the free vibration of porous functionally graded material beams with three different boundaries, namely, clamped-clamped (C-C), clamped-simply supported (C-S) and simple supported-simple supported (S-S), are calculated.The results are compared with the data in the existing literature, and the results are verified.The effects of the porosity, slenderness ratio and gradient index on the dimensionless natural frequencies of the porous functionally graded beams are discussed. |
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