Buckling And Vibration Analysis Of Viscoelastic Nanoplate With High-order Surface Stress Effects

The small size effect,the influences of high-order surface stress and spring stiffness of viscoelastic medium on the buckling behaviors of the nanoplate are studied on the basis of the Kirchhoff plate theory,the nonlocal elastic theory,the Kelvin model and Kelvin-Voigt foundation model.Meanwhile,the small size effect,the influences of high-order surface stress and spring stiffness and damping of viscoelastic medium on the vibration behaviors of the viscoelastic nanoplate are also studied on the basis of the theories mentioned above.The closed form solutions for buckling load and eigenfrequency of the rectangular nanoplate with simply supported boundary conditions are obtained by employing Navier’s approach.Numerical results show that:The buckling load of the nanoplate will decrease with the increase of nonlocal parameter.However,the buckling load of the nanoplate considering the effect of surface stress is larger than that ignoring the effect of surface stress.Additionally,the effect of the high-order surface stress on the buckling load is much more significant than that of the conventional surface stress.The small size effect can lower the values of the undamped and damped frequencies,whereas the surface stress effect can raise their values.Both the surface stress and small size effects make the damping ratio become smaller.The effects of the high-order surface stress on the undamped and damped frequencies and the damping ratio of the nanoplate are much more significant than those of the conventional surface stress.In addition,the damped frequency and damping ratio are related to the viscoelastic structural damping.The damping ratio increases and the damped frequency decreases with the increase of the viscoelastic structural damping.The spring stiffness of viscoelastic medium can raise the value of buckling load of the nanoplate.The spring stiffness of viscoelastic medium can raise the values of the undamped and damped frequencies,whereas the spring stiffness of viscoelastic medium can lower the value of the damping ratio of the nanoplate.Meanwhile,the damping ratio increases and the damped frequency decreases with the increase of the damping of viscoelastic medium.