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This paper deals with the combination of surface and couple stress theories to examine free vibrational behavior of rotating functionally graded (FG) nanobeams under axial magnetic field. The theory introduces a scale parameter based on modified couple stress theory to capture the size effects. The modified couple stress theory is a weakly nonlocal theory and introduces the stiffness-hardening effect. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved by applying an analytical solution which satisfies clamped-free boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as length scale parameter, surface energy, angular velocity, magnetic field and power-law exponent on natural frequencies of rotary FG nanobeams in detail. [ABSTRACT FROM AUTHOR]

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc. [ABSTRACT FROM AUTHOR]

In this article, free vibration of functionally graded (FG) viscoelastic nanobeams embedded in viscoelastic foundation exposed to hygro-thermal loading is investigated based on nonlocal strain gradient elasticity theory and a higher order refined beam theory which captures shear deformation influences without the need for any shear correction factor. Also, the exact position of neutral axis is determined. The visco-Pasternak foundation is consists of parallel springs and dashpots as well as a shear layer. Temperature-dependent material properties of FGM beam are graded across the thickness based on the power-law form. Hamilton's principle is used to obtain nonlocal governing equations of embedded strain gradient viscoelastic nanobeam which are solved analytically for various boundary conditions. The results are validated with those available in the literature. The impacts of visco-Pasternak foundation parameters, structural damping coefficient, hygrothermal loading, nonlocal stress parameter, nonlocal gradient parameter, power-law exponent, mode number, boundary conditions and slenderness ratio on the damping frequency of nanoscale viscoelastic FG beams are evaluated. [ABSTRACT FROM AUTHOR]