Effect of three-parameter viscoelastic medium on vibration behavior of temperature-dependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment

In this article, free vibration of functionally graded (FG) viscoelastic nanobeams resting on viscoelastic foundation subjected to hygrothermal loading is investigated employing a higher order refined beam theory which captures shear deformation influences needless of any shear correction factor. The three-parameter viscoelastic medium consists of parallel springs and dashpots as well as a shear layer. Temperature-dependent material properties of FGM beam are graded across the thickness via the power-law model. Employing non-local elasticity theory of Eringen and Hamilton's principle, non-local governing equations of a size-dependent viscoelastic nanobeam are obtained and solved analytically for various boundary conditions. To verify the reliability of the developed model, the results of the current work are compared with those available in literature. The effects of viscoelastic foundation parameters, internal damping coefficient, hygrothermal loading, non-local parameter, gradient index, mode number, and slenderness ratio on the vibrational characteristics of nanoscale viscoelastic FG beams are explored.