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In this study, the dynamic stability of double-walled carbon nanotubes (DWCNTs) conveying pulsating viscous fluid located on visco-Pasternak medium is investigated. The effects of small scale are considered using Eringen's non-local theory. The surrounding medium of DWCNT is anticipated as a visco-Pasternak foundation including the normal, shear, and damping forces. The van der Waals (vdWs) force is considered among the inner and outer layers of DWCNT. Three types of temperature changes, i.e. uniform, linear and sinusoidal temperature rise, through the thickness are studied. The equations of motion are obtained using higher order sinusoidal shear deformation shell theory (SSDT), in which the surface effects are included. Dynamical equations of DWCNT are extracted using the energy method and Hamilton's principle. Due to orthogonal conditions, the governing equations are solved based on Bolotin method. The effects of different parameters such as surface stress, non-local parameter, fluid velocity, Knudsen's number, fluid density, dimensions ratio and various temperature loadings on the dynamic stability regions of DWCNTs are discussed.

This study proposes a solution for the analysis of critical buckling load of a coupled double-layer graphene sheets (DLGSs) system resting on elastic medium. In the upper and lower parts of the system, two graphene layers, which are under van der Waals force and related to each other through an elastic medium on the basis of Pasternak and Winkler models, are utilized. The performed model is considered to be based on Eringen's nonlocal elasticity theory and sinusoidal nonlocal shear deformation theory. In addition, the properties of orthotropic plate are applied in the model. Constitutive relations and equations together with boundary conditions are derived on the basis of Hamilton's principle. Furthermore, the effect of surface stress according to Gurtin-Murdoch theory is considered. Moreover, critical buckling load for in-phase, out-of-phase, and one side fixed states subjected to in-plane forces is obtained. The results of the study reveal the minimum value of critical buckling load for in-phase state and the maximum value of that for out-of-phase state, and that the value of one side fixed state critical buckling load exists between these two states.