• Structural Engineering and Mechanics
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• 제61권5호
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• pp.563-576
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• 2017

This paper is a continuation of the investigations started in the paper by Akbarov, S.D., Guliyev, H.H and Yahnioglu, N. (2016) "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Structural Engineering and Mechanics, 57(2), 239-263, to the case where the three-layered sphere is a hollow one. Three-dimensional exact field equations of elastodynamics are employed for investigation and the discrete-analytical method is employed for solution of the corresponding eigenvalue problem. The FGM is modelled as inhomogeneous for which the modulus of elasticity, Poison's ratio and density vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies are presented and discussed. These results are also compared with the corresponding ones obtained in the previous paper by the authors. In particular, it is established that for certain harmonics and for roots of certain order, the values of the natural frequency obtained for the hollow sphere can be greater (or less) than those obtained for the solid sphere.

• Advances in nano research
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• 제6권4호
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• pp.377-397
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• 2018

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.