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| DTM analysis for free vibration of rotating FGM beams resting on elastic foundations |
| Received:August 24, 2016 Revised:November 18, 2016 |
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| DOI：10.7511/jslx201706006 |
| KeyWord:elastic foundation rotating FGM beam non-dimensional natural frequency generalized Hamilton principle Differential Transform 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 |
| 张会凯 |
兰州理工大学 理学院, 兰州 |
| 马永斌 |
兰州理工大学 理学院, 兰州 |
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| Abstract: |
| Based on Euler-Bernoulli beam theory,the governing differential equation of motion of the lateral free vibration a rotating functionally graded material (FGM) beam on elastic foundation is derived by using generalized Hamilton principle,and differential transform method (DTM) is used to transform the dimensionless governing differential equation and the boundary conditions.At the same time,the dimensionless natural frequencies of transverse free vibration of rotating FGM beam on elastic foundation at the clamped-clamped,clamped-simply supported and clamped-free three boundary conditions are determined,then the governing differential equation is degenerated to the FGM without rotation and elastic foundation.The values of first non-dimensional natural frequency with different FGM gradient index are calculated and they are completely consistent with the results by either the FEM or the Lagrange multipliers method in the literature.The results show:at the above three kinds of the boundary conditions,the dimensionless natural frequencies increase with the growth of the dimensionless rotating speed and the dimensionless elastic foundation modulus.Under a certain dimensionless rotating speed and dimensionless elastic foundation modulus,the dimensionless natural frequencies decrease along with the growth of the FGM gradient index.However,when at clamped-simply supported and clamped-free boundary conditions,the first dimensionless natural frequency is almost constant. |
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