Damping Vibration Behavior of Viscoelastic Porous Nanocrystalline Nanobeams Incorporating Nonlocal–Couple Stress and Surface Energy Effects

Abstract

Damping vibration analysis of multi-phase viscoelastic nanocrystalline nanobeams on viscoelastic medium is carried out accounting for nano-grains and nano-voids sizes. For the first time, a contribution of nonlocal, couple stress and surface energy effects is applied for vibration analysis of nanocrystalline nanobeams. In fact, couple stress theory considers grains microrotations, 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 differential transform method. 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.