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A unified formulation for thermo-mechanical vibration analysis of size-dependent Timoshenko micro-beams comprised of functionally graded materials (FGMs) with general restraints is presented. The size effect is considered by incorporating the modified strain gradient theory into Timoshenko beam theory. The thermal and mechanical properties of FGMs are related to temperature and are assumed as continuous variation along the thickness. The Mori–Tanaka estimate is used for calculation of the material properties of FGM micro-beam. The formulation is deduced on the basis of the variational principle combined with penalty function method. The displacements and rotation of the FGM micro-beam are uniformly expanded by a modified Fourier series composed of traditional cosine series and some appropriate supplementary functions. Several comparisons of the present solutions with those from existing literature confirm the validity of the current formulation. In addition, a parametric study is given to demonstrate the influence of length scale parameters, gradient indices, end restraints and temperature changes on vibration characteristic of functionally graded micro-beam.

Functionally graded multiwalled carbon nanotube (MWCNT) reinforced epoxy matrix composites are fabricated using a centrifugal method. Aggregation of the MWCNTs during the epoxy curing process is prevented using a two-step aminosilane modification. Chemical interaction of the silane with the oxidized nanotube surface is confirmed using Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy. Raman spectroscopy of acid-treated MWCNTs corroborates the formation of surface defects owing to the introduction of carboxyl groups. The mechanical and microwave absorption property gradients of the composites correspond with those produced via silane modification indicating potential application to microwave absorbing materials. The MWCNTs are better dispersed in the epoxy resin after the modification, making it possible for them to become efficiently graded in the epoxy matrix. We therefore show that it is possible to fabricate functionally graded nanofiller-reinforced materials using the centrifugal method by modifying the surface of the nanofiller.