In the present study, thermo-mechanical vibration behavior of non-uniform beams made of functionally graded (FG) porous material are investigated under different thermal loadings for the first time. It is observed that during the fabrication of functionally graded materials (FGMs) porosities and micro-voids can be occured inside the material, thus in this study vibration analysis of FG beams by considering the effect of these imperfections is performed. Material properties of the FG beam are assumed to be temperature-dependent and vary continuously through thickness direction according to a power-law scheme which is modified to approximate material properties for both even and uneven distributions of the porosities. Different thermal environmental conditions, including uniform, linear and non-linear temperature changes through the thickness direction are considered. The motion equations are derived based on the Euler-Bernoulli beam theory through Hamilton's principle and they are solved applying the differential transformation method (DTM). In order to show the accuracy of the present analysis, comparisons are made with previous researches and an excellent agreement is observed. The obtained results are presented for the thermo-mechanical vibration characteristics of the FG beams such as the influences of various temperature rises, gradient index, porosity volume fraction, taper ratio and the boundary conditions in detail.

This paper investigates free vibration characteristics of a rotating double-tapered functionally graded (FG) beam made of porous material. Material properties of the FG beam vary continuously through thickness direction according to the power-law which modified to approximate material properties for even and uneven distributions of porosities. The governing differential equations of motion are derived based on Euler–Bernoulli beam theory and using Hamilton's principle and then solved utilizing a semi-analytical technique called the differential transform method (DTM). In order to verify the competency and accuracy of the current analysis, a comparative study with previous researches is performed and good agreement is observed. Several important parameters such as power-law exponent, porosity volume fraction, taper ratios, rotational speed and slenderness ratio which have impacts on natural frequencies of such beams are investigated and discussed in detail. It is concluded that these effects play significant role on dynamic behavior of rotating double tapered FG beam. Numerical results are tabulated in several tables and figures that can serve as benchmarks for future analyses of FGM beams with porosity phases.

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