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    Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using Doublet Mechanics
    (Springer, 2018) Gul, U.; Aydogdu, M.; Gaygusuzoglu, G.
    In the present study, vibration and buckling of nanotubes (nanofibers) embedded in an elastic medium are studied. A length scale-dependent theory called Doublet Mechanics (DM) is used in the formulation. In this theory, discrete microstructure of solids is considered in the formulation and using a bottom-up approach macro level strains and stresses are obtained from microlevel strains and stresses. Taylor series expansion of the microlevel displacement is used in the definition of the micro strains. The number of terms in the Taylor series describes the microstructure of the considered solids. In this study, nanotube fibers are assumed as an Euler-Bernoulli beam embedded in an elastic medium. Simply supported and clamped boundary conditions are considered at the edges of the beams. Free vibration frequencies and critical buckling loads are obtained and compared with the classical elasticity results. It is shown that scale-dependent DM can be used at the nanolength scale.
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    WAVE PROPAGATION ANALYSIS IN BEAMS USING SHEAR DEFORMABLE BEAM THEORIES CONSIDERING SECOND SPECTRUM
    (Cambridge Univ Press, 2018) Gul, U.; Aydogdu, M.
    In this study, wave propagation in beams is studied using different beam theories like Euler-Bernoulli, Timoshenko and Reddy beam theories. Dispersion curves obtained for these beam theories are compared with the exact plane elasticity solutions. It is obtained that, there are two branches for Reddy beam theory similar to the Timoshenko beam theory. However, one branch is obtained for Euler-Bernoulli beam theory. The effects of in-plane load on Timoshenko and Reddy beam theories are examined and dispersion curves of the Timoshenko and Reddy beams are compared with exact plane elasticity solution. In Timoshenko beam theory, qualitative difference between the two spectrums has been lost with in-plane loads for some wave numbers.