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Advances in Aircraft and Spacecraft Science
  Volume 5, Number 1, January 2018 , pages 141-164

Dynamic modeling of nonlocal compositionally graded temperature-dependent beams
Farzad Ebrahimi and Ramin Ebrahimi Fardshad

    In this paper, the thermal effect on buckling and free vibration characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory through Hamilton\'s principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, aspect ratio and mode number on the critical buckling temperature and normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the thermal buckling and vibration behaviour of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.
Key Words
    thermal buckling; Timoshenko beam theory; vibration; functionally graded material; nonlocal elasticity theory
Farzad Ebrahimi: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin P.O.B. 16818-34149, Iran
Ramin Ebrahimi Fardshad: Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

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