Abstract
This article intends to investigate the free vibration damping characteristics of functionally graded viscoelastic nanobeams embedded in viscoelastic foundations using the infinite Kelvin–Voigt model of the Winkler–Pasternak type. This model is based on the nonlocal strain-driven gradient elasticity theory of Eringen. A power law model is then adopted to describe the continuous variation in the material properties of functionally graded material nanobeams. The study was carried by means of the first-order shear deformation theory with the shear correction factor using the finite element method. For the purpose of validating the developed model, it was decided to compare the results obtained with those reported about elastic nanobeams in the literature. Moreover, the influence of the power law exponent, structural damping coefficient, foundation coefficient, nonlocal parameter, and boundary conditions on the free frequency response of viscoelastic nanobeams was also investigated.
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