Size-dependent transverse vibration of viscoelastic nanoplates including high-order surface stress effect

The general governing equation for size-dependent transverse vibration of viscoelastic rectangular nanoplate with high-order surface stress effect is formulated. Using the Navier' method, the closed form solutions for vibrational frequencies of the nanoplate with simply supported boundary conditions are obtained. The small size effect and the influences of high-order surface stress and viscoelastic structural damping on the damped frequency of the nanoplate are discussed. It is demonstrated that the damped frequency and the damping ratio of the nanoplate are significantly dependent upon the small size and high-order surface stress effects. The effects of the high-order surface stress on the damped frequency and the damping ratio of the nanoplate are much more significant than those of the conventional surface stress. Moreover, the damped frequency and damping ratio are related to the viscoelastic structural damping.