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In this paper, the large-amplitude nonlinear vibration characteristics of functionally graded (FG) Timoshenko beams made of porous material is investigated for the first time. Material properties of FG porous beam are supposed to vary continuously along the thickness according to the rule of mixture which modified to approximate material properties with porosity phases. The governing equations are derived based on Timoshenko beam theory through Hamilton׳s principle and they are solved utilizing both Galerkin׳s method and the method of multiple scales. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG porous beams as compared to 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 material distribution profile, porosity volume fraction, aspect ratio and mode number on the normalized natural frequencies of the FG porous beams in detail. It is explicitly shown that the vibration behavior of a FG beams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG porous beams. [ABSTRACT FROM AUTHOR]

In this paper, the thermal effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading is investigated by presenting a Navier type solution and employing a semi analytical differential transform method (DTM) for the first time. Two kinds of thermal loading, namely, linear temperature rise and nonlinear temperature rise are studied. 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 through Hamilton׳s principle and they are solved applying DTM. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also 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, mode number and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the 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. [ABSTRACT FROM AUTHOR]