Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory

Based on a higher order refined beam model, damping vibration analysis of multi-phase viscoelastic nanocrystalline nanobeams on visco-Pasternak foundation in carried out accounting for nano-grains and nano-voids sizes. For the first time, a contribution of nonlocal and couple stress effects is applied for damping vibration analysis of nanocrystalline nanobeams. In fact, couple stress theory considers grains micro-rotations. While, nonlocal elasticity theory considers long-range interactions between the particles. Viscoelastic medium is described as infinite parallel springs as well as shear and viscous layers. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical approach. The frequencies are compared with those of nonlocal and couple stress based beams. It is observed that damping frequencies of a nanocrystalline nanobeam are significantly influenced by the grain size, grain rotations, porosities, interface, damping coefficient, surface energy, nonlocality and structural damping.