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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]

Static stability analysis of a size-dependent magneto-electro-elastic functionally graded nanoplate has an immense contribution in identification and improvement of the performance of nano-electro-mechanical systems. A refined trigonometric plate theory is employed to formulate the magneto-electro-elastic functionally graded nanoplate for the first time. Magneto-electro-elastic properties of nanoplate change in spatial coordinate based on power-law form. Regarding the small-scale effects at nanoscales, the size-dependent nonlocal continuum theory is employed to derive governing equations of the nonclassical magneto-electro-elastic functionally graded nanoplate. Analytical solution possessing functions which satisfy different boundary conditions is adopted to solve the equations. The results illustrate the size-dependent buckling behavior of magneto-electro-elastic functionally graded nanoplate affected by magnetic potential, electric voltage, various boundary conditions, small-scale parameter, material composition, plate side-to-thickness ratio, and aspect ratio. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, free vibration analysis of rotating functionally graded thick beams within the context of Timoshenko beam theory is presented. Material properties of functionally graded beam are supposed to vary exponentially along the thickness direction of the constituents. Governing equations are derived through Hamilton’s principle and they are solved applying differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several beam parameters such as constituent volume fractions, slenderness ratios, rotational speed and hub radius on vibration characteristics of the rotating thick functionally graded beam. It is concluded that these effects play significant role on dynamic behavior of rotating FG beam. Numerical results are presented to serve as benchmarks for future analyses of such beams. [ABSTRACT FROM AUTHOR]