Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory

Abstract This paper investigates damping vibration characteristics of hygro-thermally affected functionally graded (FG) viscoelastic nanobeams embedded in viscoelastic foundation based on nonlocal strain gradient elasticity theory. The modeling of nanobeam is carried out via a higher order refined beam theory which captures shear deformation influences needless of any shear correction factor. The viscoelastic foundation is consists of Winkler-Pasternak layer together with a viscous layer of infinite parallel dashpots. Power-law model is adopted to describe continuous variation of temperature-dependent material properties of FG nanobeam. The governing equations of nonlocal strain gradient viscoelastic nanobeam in the framework of refined beam theory are obtained using Hamilton’s principle and solved implementing an analytical solution for different boundary conditions. To validate the presented model, the results are compared with those of elastic nanobeams. The effects of linear, shear and viscous layers of foundation, structural damping coefficient, hygro-thermal environment, nonlocal parameter, material characteristic parameter, power-law exponent, mode number, boundary conditions and slenderness ratio on the frequency response of viscoelastic FG nanobeams are investigated.