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Structural Engineering and Mechanics Volume 59, Number 2, July25 2016 , pages 343-371 DOI: https://doi.org/10.12989/sem.2016.59.2.343 |
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Thermo-mechanical vibration analysis of temperature- dependent porous FG beams based on Timoshenko beam theory |
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Farzad Ebrahimi and Ali Jafari
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| Abstract | ||
| In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton\'s principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases. | ||
| Key Words | ||
| thermo-mechanical vibration; functionally graded beam; porous material; DTM; thermal effect | ||
| Address | ||
| Farzad Ebrahimi and Ali Jafari: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran | ||