On vibrations of functionally graded viscoelastic nanobeams with surface effects

摘要: Abstract This paper addresses the size-dependent free vibration of functionally graded viscoelastic (FGV) nanobeams including simultaneous effects microstructure rotation and surface energy for first time. Employing Bernoulli–Euler beam theory, an internal damping mechanism based on Kelvin–Voigt model is adopted to simulate behavior material. The modified couple stress theory Gurtin–Murdoch elasticity are reconsidered harnessed capture effects, respectively. local-Cauchy stress, tensors obtained incorporating measures elastic viscous behaviors nanobeam. material properties bulk FGV nanobeam assumed vary continuously in thickness direction according a power law. A variational approach basis D'Alembert's principle employed derive exactly governing differential equation associated nonclassical boundary conditions. An analytical expression derived complex natural frequencies simply supported In context linear viscoelasticity, influences different parameters such as damping, gradient index, length-scale parameter, elasticity, residual mass density, Poisson effect, thickness, slenderness ratio comprehensively discussed. results highlighted profound small size, response nanobeams.