Nonlocal vibration and biaxial buckling of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between

The general equation for transverse vibration of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between and each nanoplate subjected to in-plane edge loads is formulated on the basis of the Eringen's nonlocal elastic theory and the Kelvin model. The factors of the structural damping, medium damping, small size effect, loading ratio, and Winkler modulus and shear modulus of the medium are incorporated in the formulation. Based on the Navier's method, the analytical solutions for vibrational frequency and buckling load of the system with simply supported boundary conditions are obtained. The influences of these factors on vibrational frequency and buckling load of the system are discussed. It is demonstrated that the vibrational frequency of the system for the out-of-phase vibration is dependent upon the structural damping, small size effect and viscoelastic Pasternak medium, whereas the vibrational frequency for the in-phase vibration is independent of the viscoelastic Pasternak medium. While the buckling load of the system for the in-phase buckling case has nothing to do with the viscoelastic Pasternak medium, the buckling load for the out-of-phase case is related to the small size effect, loading ratio and Pasternak medium.