article · Mechanics of Advanced Materials and Structures
A theoretical framework evaluates the free vibration behaviour of functionally graded nanobeams exposed to thermal environments, using a third-order shear deformation beam theory. Both uniform and nonlinear temperature distributions are considered. Within the beam, thermo-elastic coefficients and the nonlocal parameter are graded across the thickness according to a power-law distribution, incorporating small-scale effects via Eringen's nonlocal elasticity. Governing equations obtained through Hamilton's principle are solved analytically. Comparisons with nonlocal Euler-Bernoulli and Timoshenko beam models demonstrate that this analytical approach accurately predicts vibration frequencies. Detailed results examine how material graduation, nonlocal parameters, mode numbers, slenderness ratios, and thermal loading influence thermo-mechanical vibrations. The resulting analysis supports the understanding of structural elements subject to thermal loads across demanding operational settings.
Engineered components at the nanoscale experience distinct thermal and mechanical stresses that standard beam theories cannot accurately capture. Providing an analytical model that incorporates shear deformation and graded material properties allows engineers to predict vibration responses more precisely. This knowledge is important for designing robust nanoscale structural elements operating under severe temperature variations.
The analytical model is relevant to design and analysis software for aerospace, mechanical, and nuclear engineering sectors where nanoscale components face thermal stress. Potential users include structural analysts, simulation tool developers, and advanced materials researchers. The work represents early-stage analytical research, needing physical validation and integration into engineering software before direct industrial adoption.
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In the present research, free vibration study of functionally graded (FG) nanobeams with graded nonlocality in thermal environments is performed according to the third-order shear deformation beam theory. The present nanobeam is subjected to uniform and nonlinear temperature distributions. Thermo-elastic coefficients and nonlocal parameter of the FG nanobeam are graded in the thickness direction according to power-law form. The scale coefficient is taken into consideration implementing nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of nonlocal Euler–Bernoulli and Timoshenko beam models, and it is revealed that the proposed modeling can accurately predict the vibration frequencies of the FG nanobeams. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio, and thermal loading in detail. The present study is associated to aerospace, mechanical, and nuclear engineering structures that are under thermal loads.
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DOI: 10.1080/15376494.2017.1285458
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