Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects

This article deals with the free vibration investigation of nonlocal strain gradient-based viscoelastic functionally graded (FG) nanobeams on viscoelastic medium considering surface stress effects. Nonlocal strain gradient theory possesses a nonlocal stress field parameter and a length scale parameter for more accurate prediction of mechanical behavior of nanostructures. Surface energy effect is incorporate to the nonlocal strain gradient theory employing Gurtin–Murdoch elasticity theory. Thermo-elastic material properties of nanobeam are graded in thickness direction using power-law distribution. Hamilton’s principal is utilized to obtain the governing equations of FG nanobeam embedded in viscoelastic medium. The effects of surface stress, length scale parameter, nonlocal parameter, viscoelastic medium, internal damping constant, thermal loading, power-law index and boundary conditions on vibration frequencies of viscoelastic FGM nanobeams are discussed in detail.